Meaning at the Planck scale? Contextualized word embeddings for doing history, philosophy, and sociology of science
Paper • 2411.14073 • Published
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There are several reasons that make it desirable to improve mathematical tools used in the nonlocal theory of highly singular quantum fields with an exponential or faster high-energy behaviour. First of all string theory gives us new indications [1-3] that the concept of space-time manifold is only approximate and vali... | 1,907 | hep-th/9211099 | 36,668 | 1,992 | 11 | 24 | false | true | 1 | UNITS |
This does not yet look like the functional Schroedinger equation for the scalar field. However, we may recall that formally the expression inside the square root is divergent. However, it may not be actually divergent because in computing (66) we have assumed that the scalar field is slowly varying on the scale of the ... | 937 | gr-qc/9301016 | 44,883 | 1,993 | 1 | 15 | false | true | 2 | UNITS, UNITS |
These results make possible the construction of a correspondence between any three geometry whose curvature is small in Planck units and a diffeomorphism invariant state of the gravitational and matter fields. This correspondence relies on the approximation of the classical geometry by a piecewise flat Regge manifold, ... | 611 | gr-qc/9302011 | 49,758 | 1,993 | 2 | 10 | false | true | 1 | UNITS |
For polynomial actions a lot of attention has been given to the existence of a pseudo Fokker-Planck (F-P) equation which describes the dynamics of a possibly equivalent complex valued weight function [CIT]. In earlier investigations especially the spectrum of this operator played a major role [CIT]. But statements on t... | 1,426 | hep-lat/9312003 | 121,625 | 1,993 | 12 | 1 | false | true | 1 | FOKKER |
What are the exact conditions under which the semiclassical Hamilton-Jacobi equation is valid? The first, obvious, condition is that the expectation value of ${\cal H}$ with respect to the state satisfying the approximate Schrödinger equation be *small* compared to the other terms in (4.15). This came out in a natural ... | 849 | gr-qc/9312015 | 124,109 | 1,993 | 12 | 9 | true | true | 1 | UNITS |
In this newly defined notation, the overdamping constraint is written as FORMULA and the density perturbation constraint is FORMULA Using the equation of motion [1.8] and the relation FORMULA we can write the condition that the universe is dominated by potential energy rather than kinetic energy (Eq. [1.10]) in the for... | 878 | astro-ph/9401006 | 131,650 | 1,994 | 1 | 7 | true | false | 1 | UNITS |
In Section REF we describe the stochastic inflation formalism [CIT] for Jordan--Brans--Dicke inflation, see also [CIT]. The Brownian motion of the scalar fields in de Sitter space can be written as a Langevin equation for the coarse-grained fields with an effective white noise generated by quantum fluctuations. The ass... | 1,285 | astro-ph/9401042 | 136,744 | 1,994 | 1 | 24 | true | true | 3 | FOKKER, FOKKER, FOKKER |
Chaotic inflation scenario [CIT] has brought two surprises. First of all, it was realized that inflation can occur even if there was no thermal equilibrium in the early Universe, and even if the effective potential $V(\phi)$ does not have any maximum at all, or if its maximum is not sufficiently flat. In particular, ch... | 1,143 | hep-th/9402115 | 145,134 | 1,994 | 2 | 20 | true | true | 1 | UNITS |
Due to the existence of a minimum proper interval, the notion of event loses one of its characteristic features: it is no longer an invariant concept [CIT]. The uncertainty in the radius of the black hole horizon may be interpreted as giving rise to a membrane, a stretched horizon, from the point of view of an observer... | 1,446 | gr-qc/9403008 | 147,485 | 1,994 | 3 | 2 | false | true | 1 | UNITS |
In addition, we should not forget that the fermion masses are much closer to the weak scale, rather than the Planck scale, so it does not seem to us too unnatural trying to explain them in terms of physics coming in at the weak scale, rather than expecting "Planck-\" or higher-scale physics to "feed down\" their effect... | 872 | hep-ph/9403220 | 147,968 | 1,994 | 3 | 3 | false | true | 4 | UNITS, UNITS, UNITS, UNITS |
Inspired by the work of Wheeler among others, we have studied the problem of quantum measurements of space-time distances by applying the general principles of quantum mechanics as well as those of general relativity. Contrary to the folklore, the minimum error in the measurement of a length is shown to be proportional... | 609 | hep-th/9406110 | 182,853 | 1,994 | 6 | 16 | false | true | 1 | UNITS |
Apart from the general laws of motion, one requires a set of initial conditions for the universe. Early models of inflation postponed the issue by assuming that the universe started in a very hot state that supercooled in a metastable vacuum, which then decayed to the true vacuum [CIT]. But in fact, the only reasonable... | 1,285 | astro-ph/9407087 | 197,391 | 1,994 | 7 | 27 | true | true | 2 | UNITS, UNITS |
On the basis of our experience with a wide class of potentials (we have found similar effects for the quadratic and quartic potentials of chaotic inflation) we want to conclude that the presence of quantum inflation seems to be a generic feature of field theoretical models addressing Planck scale physics and it may be ... | 387 | hep-ph/9408267 | 202,113 | 1,994 | 8 | 10 | false | true | 1 | UNITS |
Expression (33) means that quantum corrections result in the shifting the horizon radius by the Planck distance. For the charged black hole with $Q<M<\sqrt{\frac{25}{24}}Q$ the quantum corrections decrease the horizon radius while for $M>\sqrt{\frac{25}{24}}Q$ it is increasing. The quantum corrected entropy is determin... | 576 | hep-th/9408068 | 202,792 | 1,994 | 8 | 12 | false | true | 2 | UNITS, UNITS |
This is the second part of a binary paper discussing Fokker-Planck models matched with observations of the globular cluster NGC 6397. In the first paper (Drukier 1994; Paper A), the details of the modeling and comparison techniques were discussed, as was an overview of results of the over 1000 models run. Briefly, the ... | 1,153 | astro-ph/9409087 | 217,897 | 1,994 | 9 | 29 | true | false | 2 | FOKKER, FOKKER |
Another possibility is that the Universe was large and hot from the very beginning, and it became inflationary only when its thermal energy density $\sim T^4$ dropped below $V(\phi)$. Inflation begins at this stage only if the Universe at this moment was sufficiently homogeneous on a scale greater than $\Delta x \sim H... | 1,701 | hep-th/9410082 | 222,706 | 1,994 | 10 | 12 | true | true | 5 | UNITS, UNITS, UNITS, UNITS, UNITS |
The superstring dilaton also demonstrates this property of dynamical Planck fields. A kinetic inflation from the dilaton of superstring theories was discussed independently in Refs. [CIT]. Recently, there have been interesting studies of an inflating superstring cosmology in higher dimensions (see for example [CIT]). I... | 640 | gr-qc/9411041 | 235,570 | 1,994 | 11 | 15 | true | false | 1 | OTHER |
On more phenomenological grounds, there is also a problem of scales which requires further studies. The scalar field which is part of the Riemann connection and is related to the distance between the two sheets of space--time, pertaining to the intrinsic structure of the latter, has as a natural scale, the Planck lengt... | 851 | gr-qc/9503040 | 285,636 | 1,995 | 3 | 22 | false | true | 2 | UNITS, UNITS |
A reason to consider finite temperature quantum field theories is mainly based on the recent developments of cosmological models. According to the standard Big-Bang cosmology and the more recent inflationary models, the very early universe has passed through a phase of thermal equilibrium at very high temperature and d... | 1,511 | hep-th/9505061 | 306,358 | 1,995 | 5 | 10 | false | true | 1 | UNITS |
Here we point out that the time evolution in 4D quantum gravity is described by a Langevin equation for 3-geometries in terms of the Ashtekar's canonical field variables by showing that the corresponding Fokker-Planck hamiltonian operator exactly recovers the hamiltonian of 4D Euclidean quantum gravity in the gauge $N=... | 624 | hep-th/9509087 | 362,126 | 1,995 | 9 | 18 | false | true | 1 | FOKKER |
We consider a 2-parameter class of solvable closed superstring models which `interpolate' between Kaluza-Klein and dilatonic Melvin magnetic flux tube backgrounds. The spectrum of string states has similarities with Landau spectrum for a charged particle in a uniform magnetic field. The presence of spin-dependent `gyro... | 1,175 | hep-th/9510041 | 370,965 | 1,995 | 10 | 7 | false | true | 1 | UNITS |
This model contains a similar structure to the "hybrid\" inflation models, proposed by Linde and studied by Copeland, Liddle, Lyth, Stewart, and Wands [CIT]. The fact that the standard dimensional naturalness arguments for the number of $e$-foldings and for $\delta \rho/\rho$ do not apply, and that the Hubble scale dur... | 1,058 | hep-ph/9601296 | 419,337 | 1,996 | 1 | 18 | true | true | 1 | UNITS |
We have shown that with more than one field it is possible to construct models of inflation with no small parameters. Furthermore, the mass scales which seem to most naturally appear in these models are of order $m_{3/2}$, about 1 TeV, and $M_I$, about $10^{11}$ GeV, leading to a natural association with supersymmetric... | 795 | hep-ph/9601296 | 419,367 | 1,996 | 1 | 18 | true | true | 1 | UNITS |
Supersymmetry is an elegant extension of the standard model of particle physics. It is the only so-far "unused" symmetry of the Poincare group and has the virtue of protecting the weak scale against radiative corrections from GUT and Planck scale. Local supersymmetry appears to be an attractive route towards unifying a... | 780 | astro-ph/9603026 | 443,388 | 1,996 | 3 | 6 | true | false | 1 | UNITS |
Now in the gauged NJL model, QCD plus four-fermion interaction (REF), essentially the same mechanism as the above is operative. Based on the very slowly damping solution of the ladder SD equation (REF) and the PS formulas, (REF) and (REF), MTY [CIT] predicted $m_t$ and $\delta \rho$ as the *decreasing function of cutof... | 417 | hep-ph/9603277 | 446,175 | 1,996 | 3 | 12 | false | true | 1 | UNITS |
We also consider the particular initial conditions problem faced by a spatially closed FRW universe, which in the absence of fine-tuning will typically have a lifetime on the order of the Planck scale [CIT]. This problem persists in the presence of inflation: although inflation can begin at the Planck scale there is no... | 540 | hep-th/9605173 | 487,880 | 1,996 | 5 | 23 | true | true | 2 | UNITS, UNITS |
Notice that postulate 1 already adds the Planck's constant to classical physics. Consider a classical system described by a variable $q$ that takes bounded but continuous values; for instance, the position of a particle. Classically, the amount of information we can gather about it is infinite: we can locate its state ... | 1,005 | quant-ph/9609002 | 550,042 | 1,996 | 8 | 31 | false | true | 3 | CONSTANT, CONSTANT, CONSTANT |
Regardless of the relative sizes of $G$ and $l$, the entropy is always minimized for $A_+ \leq G$. If we assume $G<<l$ then (REF) is solved as $A_{+min}={2\over 3}G$, However if $G >> l$, then (REF) becomes (for $\mu=0$, say) $A_+/G \simeq e^{-A_+/l} < 1$. In either case, the minimum of the entropy occurs for a hole wh... | 1,200 | hep-th/9609085 | 555,824 | 1,996 | 9 | 10 | false | true | 1 | UNITS |
We gratefully acknowledge many fruitful interactions with Marcela Carena, Mariano Quiros, and Carlos Wagner. We also appreciate useful conversations with Damien Pierce and Fabio Zwirner. Two of us (HEH and RH) would like to thank the Institute for Theoretical Physics in Santa Barbara for their partial support under the... | 754 | hep-ph/9609331 | 557,235 | 1,996 | 9 | 12 | false | true | 1 | MPS |
Since the metric (REF) is a one-loop approximation, it is valid only in the region where $R l{}_{P}{}^{2} < 1$ (since the loop-expansion of the effective metric is in $\left\langle T{}^{n}\right\rangle$, which is of the order of $(Rl{}_{P}{}^{2}){}^{n}$). This gives that $r_{AH} > {\sqrt 2}l_P$, which is the expected P... | 909 | hep-th/9611219 | 607,063 | 1,996 | 11 | 26 | false | true | 2 | UNITS, UNITS |
The pattern of variations in the intensity of magnetodipole losses is studied with the relativistic effect of magnetic-field dissipation during collapse into a black hole taken into account. A burst-type solution can be obtained both for a direct collapse and for the formation of a rapidly-rotating, self-gravitating ob... | 1,069 | astro-ph/9703006 | 664,920 | 1,997 | 3 | 1 | true | false | 1 | UNITS |
3. **Nearly scale-invariant spectrum of gravitational waves.** These gravitational waves have wavelengths from ${\cal O}(1\rm,km)$ to the size of the present Hubble radius and beyond. Described in terms of a power spectrum for the dimensionless gravity-wave amplitude at early times, $P_T(k) \equiv \langle |h_k|^2 \rang... | 1,103 | astro-ph/9703196 | 681,523 | 1,997 | 3 | 31 | true | true | 1 | UNITS |
The link between black holes and Planck scale phenomena was already suggested in paperI, and it has been investigated here how very small and very large scale physics are linked. The existence of a charge threshold at which the QGUT symmetry is broken, is equivalent to a quiescent and stable quantum foam which derives ... | 543 | gr-qc/9704036 | 691,576 | 1,997 | 4 | 14 | false | true | 2 | UNITS, UNITS |
Our present view of things is quite different. The renormalization group philosophy can be applied to the standard model itself. Imagine that we have a unified theory whose characteristic energy scale, $\Lambda$, is very large or whose characteristic distance scale, $\hbar c /\Lambda$, is very small (say the Planck len... | 2,372 | hep-th/9704139 | 695,388 | 1,997 | 4 | 18 | false | true | 2 | UNITS, UNITS |
In keeping with the analysis of the previous section we discuss thermalization induced by synchrotron self--absorption using the Fokker--Planck equation. Instead of attempting to solve the complete integrodifferential equation (eq. [REF]), we check for consistency by assuming that the (thermal) synchrotron radiation is... | 484 | astro-ph/9705067 | 708,557 | 1,997 | 5 | 9 | true | false | 2 | FOKKER, FOKKER |
An adjoint alone is not sufficient to break $SO(10)$ to the Standard Model group, $G_{SM}$, and in particular cannot reduce the rank of the group. This requires either spinorial Higgs (${\bf 16} + \overline{{\bf 16}}$) or rank-five antisymmetric tensor Higgs (${\bf 126} + \overline{{\bf 126}}$). As the latter tend to d... | 617 | hep-ph/9705366 | 716,045 | 1,997 | 5 | 20 | false | true | 1 | UNITS |
Now under the above strong energy condition we shall prove the relation as FORMULA where $t$ may be taken to be any time between the Planck time and the decoupling time. We take the standpoint that the matter content of the Universe is well understood after the big bang nucleosynthesis. In order to evaluate the integra... | 867 | gr-qc/9707043 | 765,316 | 1,997 | 7 | 18 | true | false | 2 | UNITS, UNITS |
Finally, as easily seen from the Table (REF) that all interesting effects of the d-term are proportional to the value of ${\delta_{GS}}$ hence quickly become unimportant when the mass scale of the F-I parameter becomes smaller than $M_{planck}$. Also, after supersymmetry breaking induced by some third party one can hav... | 568 | hep-ph/9708410 | 789,880 | 1,997 | 8 | 20 | false | true | 1 | UNITS |
Concerning the unification of the gauge couplings, string theory is more powerful than field theory because now also gravity is fully unified with the gauge interactions. In particular, in the heterotic string at tree level at the unification scale one finds [CIT] a relation between the Newton's constant $G_N$, the str... | 1,697 | hep-th/9708105 | 790,029 | 1,997 | 8 | 20 | false | true | 2 | UNITS, UNITS |
For the case when one adds the most general Planck scale interaction one finds that fixing the textures in the Higgs doublet sector does not uniquely fix the textures in the Higgs triplet sector [CIT]. One needs a dynamical principle to do so. One possibility suggested is to extend supergravity models to include not on... | 1,022 | hep-ph/9708469 | 793,581 | 1,997 | 8 | 26 | false | true | 4 | UNITS, UNITS, UNITS, UNITS |
We now return to the blanks in discovery mentioned in Sec.1. The blanks have remained inspite of the tremendous activity in HEP in the past two decades. The biggest loophole in standard model is the omission of gravitation, the most important force of nature. Hence, it is now recognized that *Quantum Gravity (QG) is th... | 455 | hep-ph/9709212 | 793,604 | 1,997 | 8 | 26 | false | true | 1 | UNITS |
An enforced hadronisation can be a consequence of an external or internal disturbance, leading to an expansion (or split-up) of the object to a density (or mass) well below that for hadronisation. A simple cooling of the object due to Planck radiation will not cause a hadronisation, once we assume that quark matter rem... | 358 | astro-ph/9802236 | 937,105 | 1,998 | 2 | 18 | true | true | 1 | LAW |
: A direct implementation of the idea that the mysteries of quantum gravity and the mysteries of quantum mechanics can be related is Penrose's suggestion that the wave function collapse may be a gravitational phenomenon. Penrose's idea is that there may be a nonlinear dynamical mechanism that forbids quantum superposit... | 1,730 | gr-qc/9803024 | 951,110 | 1,998 | 3 | 5 | false | true | 3 | UNITS, UNITS, UNITS |
Within the context of supergravity-coupled supersymmetry, fields which are gauge and global singlets are usually considered anathema. Their vacuum expectation values are shifted by quadratically divergent tadpole diagrams which are cutoff at the Planck scale, destabilizing the classical potential and driving the single... | 1,001 | hep-ph/9803310 | 955,073 | 1,998 | 3 | 11 | false | true | 1 | UNITS |
Composite Higgs loop effects in the top mode standard model are discussed by using the Miransky-Tanabashi-Yamawaki (MTY) approach based on the Schwinger-Dyson equation. The top mass is obtained as 179 GeV for the Planck scale cutoff (\Lambda \simeq 10^{19} GeV). This result is different from that of the Bardeen-Hill-Li... | 1,146 | hep-ph/9804435 | 992,441 | 1,998 | 4 | 28 | false | true | 1 | UNITS |
Using superfluid phases of $^3$He one can simulate a broad spectrum of phenomena related to the quantum vacuum. We discussed only few of them. On the conceptual level the lessons of $^3$He-A suggest: The gravity is the property of quantum "Planck matter\" in the classical low-energy limit. Gravitational field arise as ... | 908 | cond-mat/9806010 | 1,022,495 | 1,998 | 6 | 1 | false | true | 4 | UNITS, UNITS, UNITS, CONSTANT |
The low-energy limit of the theory corresponds to the regime when the curvature radius $L$ of the spacetime ${\cal M}$ is much greater than the Planck length $m_{Pl}^{-1}$. In this limit the effective action $\Gamma$ of the theory can be expanded in the curvature. The terms in this series are local and the leading term... | 856 | hep-th/9806078 | 1,033,472 | 1,998 | 6 | 10 | false | true | 2 | UNITS, UNITS |
Case ii), in which $m_{\tilde{q}} \ll m_{\tilde{g}}$, cannot be realized in the framework considered here, in which the soft SUSY breaking terms are introduced at the Planck scale. This is due to the fact that the evolution from the Planck to the electroweak scale forbids such a mass hierarchy. In fact, neglecting the ... | 1,435 | hep-ph/9808328 | 1,093,712 | 1,998 | 8 | 14 | false | true | 3 | UNITS, UNITS, UNITS |
In order to keep the energy finite, which from Eq. REF(#psc){reference-type="eqref" reference="psc"} and on dimensional ground scales as $R_l/l_p^2$, we should also rescale the Planck length (and any other length) as $l_{p,s} = e^{-\beta/2} l_p$. Altogether, M-theory with Planck length $l_p$ on the light-like circle of... | 714 | hep-th/9809039 | 1,113,130 | 1,998 | 9 | 7 | false | true | 3 | UNITS, UNITS, UNITS |
The Planck satellite will explore a range $\Delta \ln k\simeq 6$ of scales, and will measure $n$ with an accuracy of around $.01$. This means that a scale-dependence $|dn/d\ln k|\mathrel{\rlap{\lower 4pt\hbox{\hskip 1pt$\sim$}} \raise 1pt\hbox{$>$}}2\times 10^{-3}$ should be observable by Planck. | 297 | hep-ph/9809562 | 1,133,890 | 1,998 | 9 | 28 | true | true | 2 | MISSION, MISSION |
Using our cosmological model as given above, we have calculated the expected precision to which $x \equiv \alpha/\alpha_0$ can be determined. The results of this calculation have been shown in Fig. 3 as a function of the maximum measured $l$-value. We note here that $l_{\rm max}({\rm MAP}) \simeq 1000$ and $l_{\rm max}... | 668 | astro-ph/9810102 | 1,142,697 | 1,998 | 10 | 7 | true | true | 1 | MISSION |
Allowing for the possibility of large extra dimensions, the fundamental Planck scale $M$ could be anywhere in the range $\TeV\lsim M\lsim \mpl$, where $\mpl=2.4\times 10^{18}\GeV$ is the four-dimensional Planck scale. If $M\sim\TeV$, quantum corrections would not destabilize the Higgs mass even if there were no supersy... | 784 | hep-ph/9810320 | 1,146,773 | 1,998 | 10 | 11 | false | true | 2 | UNITS, UNITS |
2. Next, we remark in passing on another fascinating connection between the two derived scales, $M_W$ and $M_{Planck}$, which are generated from the two fundamental scales of the model, $M_s$ and $M_c$. If we write $\alpha' \sim 1/M_s^2$ then $M_W$ and $M_{Planck}$ are related one to the other by $M_W= 1/(\alpha 'M_{Pl... | 539 | hep-ph/9810535 | 1,165,990 | 1,998 | 10 | 29 | true | true | 4 | UNITS, UNITS, UNITS, UNITS |
> The hypothesis is considered that the vacuum is a Lorentz non-invariant foam in which translational symmetry is spontaneously broken at the Planck or grand unification scale. This could possibly be observed via Rayleigh scattering of ultrahigh energy quanta, and it appears to be ruled out for spin 1/2 leptons and ind... | 885 | astro-ph/9811020 | 1,169,142 | 1,998 | 11 | 2 | true | true | 4 | UNITS, UNITS, UNITS, UNITS |
Using above expressions we find $S/N=8$ for $\Omega_m=0.4$ open model and $S/N=13$ for $\Omega_m=0.2$ open model, both for Planck noise and beam properties using $f_{sky}=0.7$. Corresponding numbers for MAP are 3.5 and 7. Both MAP and Planck will thus be able to usefully constrain open models with $\Omega_m<0.4$, which... | 1,789 | astro-ph/9811123 | 1,175,300 | 1,998 | 11 | 8 | true | false | 6 | MISSION, MISSION, MISSION, MISSION, MISSION, MISSION |
A quantum elementary system is described by a complex wave field $\psi (\vec{x}, t)$ which, in the non-relativistic limit, satisfies the Schrödinger equation FORMULA where H is the hamiltonian operator FORMULA $U$ being the (external) potential experienced by the system of mass $m$ (in this paper we use natural units, ... | 939 | quant-ph/9902019 | 1,262,973 | 1,999 | 2 | 5 | false | true | 1 | CONSTANT |
Note that this relation survives in the Maldacena limit ($\Delta T \Delta U>1$), since FORMULA This explains the dual relation between the two different length scales determined by the mass of the open strings stretched between D-branes, on one hand, and the transverse distance between the branes, on the other. As disc... | 1,022 | hep-th/9902200 | 1,284,451 | 1,999 | 2 | 26 | false | true | 2 | UNITS, UNITS |
From the PICD, the minimum *SIRTF* background (which occurs at the ecliptic pole for wavelengths considered here), $b(\lambda$) is computed as FORMULA where $B_\lambda (T)$ is the Planck function for a temperature of $T$,K. The first term is due to scattered sunlight from zodiacal dust, the second and third terms to th... | 535 | astro-ph/9903067 | 1,288,235 | 1,999 | 3 | 3 | true | false | 1 | LAW |
In this paper, we present a simple and systematic method to reproduce these results by using the fluctuation-dissipation theorem [CIT] which is a basis of statistical mechanics for irreversible processes when the systems are slightly away from thermal equilibrium. This theorem states the relation between the spontaneou... | 860 | hep-th/9903062 | 1,291,848 | 1,999 | 3 | 8 | false | true | 1 | LAW |
Fortunately there are two crucial structural features to be exploited here. As noted above the pointing matrix $A$ is usually very sparse, with only ${\cal N}_{\alpha}$ non-zero entries in each row. For simple scanning strategies such as MAXIMA, BOOMERanG and PLANCK, ${\cal N}_{\alpha} = 1$, with a single 1 in the colu... | 1,264 | astro-ph/9903204 | 1,298,062 | 1,999 | 3 | 13 | true | false | 1 | MISSION |
An unusual point of the inequality (REF) is that the minimal spatial length $\delta x$ has a positive correlation with the time interval $T$. Although it seems as if the left-hand side of (REF) can be made arbitrarily small, we cannot detect an arbitrarily small spatial length scale. To show this, let us suppose a test... | 708 | hep-th/9903146 | 1,303,069 | 1,999 | 3 | 17 | false | true | 1 | STAR |
Before getting into the details of the fermion masses and mixings in the Standard Model, we first discuss in general the possible suppressions of couplings we may get in such a scenario. In addition to the usual Planck mass suppression for the higher dimensional operators, the suppressions may also come from the large ... | 446 | hep-ph/9904252 | 1,323,086 | 1,999 | 4 | 6 | false | true | 1 | UNITS |
The graviton including its excitations in the extra dimensions can couple to the SM particles on the brane with an effective strength of $1/M_S$ (instead of $1/M_G$) after summing the effect of all excitations collectively, and thus the gravitation interaction becomes comparable in strength to weak interaction at TeV s... | 1,146 | hep-ph/9904510 | 1,346,584 | 1,999 | 4 | 30 | false | true | 1 | UNITS |
For very light masses ($S>150$), numerical investigations of the ratio $R_Q/R_{cl}$ as a function of redshift $z$, using Eq. (REF) with $\mid \overline{\xi}\mid \simeq 1$, reveal that there are two distinct regimes for which this ratio is close to or larger than 1. The first such regime occurs at extremely high redshif... | 1,152 | gr-qc/9905031 | 1,354,052 | 1,999 | 5 | 10 | true | true | 1 | EPOCH |
A simple way to see that the D6 brane worldvolume theory does not decouple from the bulk is to note that now in the decoupling limit we keep $g_{YM}^2 \sim g_s l_s^3$ fixed. When we lift the D6 branes solution to M theory, this means that the eleven dimensional Planck length $l_p^3 = g_s l_s^3$ remains fixed, and there... | 938 | hep-th/9905111 | 1,359,555 | 1,999 | 5 | 14 | false | true | 1 | UNITS |
On the other hand, although the Fokker-Planck method requires more assumptions and approximations, it is much less expensive and gives statistically correct results. These features are critically beneficial, not only when the study is meant for a parameter survey, but also when statistically stable results without rand... | 613 | astro-ph/9905325 | 1,370,244 | 1,999 | 5 | 26 | true | false | 2 | FOKKER, FOKKER |
Crucial to the string interpretation of the Fokker--Planck Hamiltonian is a consistency check, equivalent to diffeomorphism invariance on the string worldsheet [CIT]. In the case of the loop operator, it is a generalization of the derivation given in [CIT] (Sect. 3) that the consistency of the string interpretation is ... | 974 | hep-th/9906052 | 1,382,811 | 1,999 | 6 | 7 | false | true | 1 | FOKKER |
Due to their relative isolation, lack of observable interstellar gas and due to their symmetry globular clusters are well approximated by simplified theoretical models. Since the relaxation timescale is long compared to the dynamical time they develop through a sequence of dynamical (virial) equilibria. The fundamental... | 902 | astro-ph/9906155 | 1,383,516 | 1,999 | 6 | 8 | true | false | 2 | FOKKER, FOKKER |
FORMULA with Planck mass $m_{pl}$. Numerically, $R_a=1.6\times10^8,M_{12}^{-1},m_5^{-2},\mbox{cm}$ where $M_{12}\equiv M_a/10^{-12},M_{\odot}$ and $m_5\equiv m_a/10^{-5},\mbox{eV}$. A similar formula holds even without the limit but with a minor modification of numerical coefficient. It turns out that the axionic boso... | 617 | hep-ph/9906353 | 1,389,412 | 1,999 | 6 | 14 | false | true | 1 | UNITS |
The trends toward the flatter mass function with time are clearly shown in this figure. The global mass function changes slowly in the early phase of the evolution, and rather abruptly in the late phase. The mass function within the half-mass radius changes more rapidly than the global mass function. The model with sma... | 574 | astro-ph/9909006 | 1,470,375 | 1,999 | 9 | 1 | true | false | 1 | FOKKER |
From the point of view of applications to the recently proposed [CIT] large extra dimensions scenario, the most important property of our solutions is that they are characterized by nontrivial "warp factors\" that affect the values of the parameters of the world-volume theories [CIT]. In particular, the usual relation ... | 741 | hep-th/9909199 | 1,500,063 | 1,999 | 9 | 28 | false | true | 1 | UNITS |
The sensitivity of a $\overline{p}$ decay search to the presence of a CPT violating interaction has been characterized by considering a dimension-$n$ CPT-violating quantum field operator ($n > 4$) with characteristic mass scale $m_X$. Dimensional analysis then provides the estimate [CIT] $m_p \tau_{,\overline{p}} \sim ... | 618 | hep-ex/9910013 | 1,509,760 | 1,999 | 10 | 6 | false | true | 1 | UNITS |
We can carry out a Fokker-Planck expansion (eq. [REF]) of the kinetic equation (REF) with the $P(\nu\rightarrow\nu^\prime)$ kernel derived in this paper (eq. [REF]). The coefficients in equation (REF) depend on the moments of the kernel, which are given by equation (REF). As a result, we obtain the generalized (for the... | 376 | astro-ph/9910280 | 1,518,905 | 1,999 | 10 | 15 | true | false | 1 | FOKKER |
We now introduce a pseudo NG chiral superfield $\Phi(x,\theta)$ whose boson components consist of the axion field ${\cal A}(x)$ and its scalar partner, saxion ${\cal B}(x)$. We consider that the NG superfield is produced by a spontaneous breakdown of some global symmetry at the Planck scale $F_{\cal A} \simeq 2\times 1... | 688 | hep-ph/9911324 | 1,550,714 | 1,999 | 11 | 12 | true | true | 1 | UNITS |
We investigate the generation of fields from other fields by scalar coupling assuming the priority of the fields in comparison with their sources. This kind of field generation is only possible for fields with a non-spherical configuration. Therefore, the spherical symmetry of all these fields is generally broken.\ Thi... | 1,943 | hep-th/9911250 | 1,569,897 | 1,999 | 11 | 30 | false | true | 1 | UNITS |
Due to the Heisenberg uncertainty principle the scale of energy (frequency) and the lifetime of the unvierse are related as FORMULA the scale of momentum projection $p_x$ and the scale of length $a_x$ are related as FORMULA Thus, within the framework of quantum mechanics, the evolution of the universe is governed by th... | 1,126 | astro-ph/9912277 | 1,584,733 | 1,999 | 12 | 14 | true | false | 2 | UNITS, UNITS |
A model of reionization is therefore, in principle, eminently testable. Current detections of the first Doppler peak in the CMB's temperature anisotropies limit the total optical depth to electron scattering, $\tau_{e}$, such as may arise from reionization, to be $\tau_e \la 1$ [CIT]. Future experiments such as the *Ne... | 730 | astro-ph/9912401 | 1,592,148 | 1,999 | 12 | 18 | true | false | 1 | MISSION |
We consider the evolution of the Affleck-Dine scalar during D-term and F-term inflation and solve the combined slow-roll equations of motion. We show that for a typical case, where both the Affleck-Dine scalar and inflaton initially have large values, in D-term inflation the Affleck-Dine scalar is driven to a fixed val... | 1,283 | hep-ph/9912478 | 1,596,201 | 1,999 | 12 | 22 | true | true | 1 | MISSION |
A fundamental problem in supergravity and superstring theories is the stabilization of moduli fields, particularly the dilaton. Perturbatively, $\Phi\equiv {\rm exp}(\lambda \phi)$ (the dilaton) has no potential, although it does not behave as a free field because it has non-linear couplings to the kinetic energy of th... | 1,345 | hep-th/0001112 | 1,625,324 | 2,000 | 1 | 19 | true | true | 2 | UNITS, UNITS |
In recent work on experimental tests of quantum-gravity-motivated phenomenological models, a significant role has been played by the so-called ``$\kappa$'' deformations of Poincar\'e symmetries. Sensitivity to values of the relevant deformation length $\lambda$ as small as $5 \cdot 10^{-33}m$ has been achieved in recen... | 828 | hep-ph/0001305 | 1,634,987 | 2,000 | 1 | 28 | false | true | 1 | UNITS |
The above procedure of $T$ dualization has the nice property to lead to a finite $D-1$ dimensional Planck mass. Indeed, whereas in the original solution it would be: FORMULA which diverges near infinity, our solution that throws away the region near infinity and paste a copy of the region near the origin, naturally giv... | 797 | hep-th/0002130 | 1,659,524 | 2,000 | 2 | 16 | false | true | 3 | UNITS, UNITS, UNITS |
Future CMB missions such as MAP and Planck could strengthen these constraints considerably. The optical depth resolution of MAP is expected to be 0.022, and of Planck is expected to be 0.004 (Zaldarriaga, Spergel, & Seljak 1997; Bouchet, Prunet, & Sethi 1999; Eisenstein, Hu, & Tegmark 1999). Since the existence of a Ly... | 1,222 | astro-ph/0003176 | 1,683,885 | 2,000 | 3 | 13 | true | false | 3 | MISSION, MISSION, MISSION |
Most measurements of small-angle CMB anisotropy are being done at high radio frequencies (in the 15--90 GHz range) where Galactic and extragalactic contaminants are a minimum. However, the high-frequency detections of small-angle anisotropy, which have to-date been Sunyaev-Zeldovich (S-Z) decrements towards clusters of... | 959 | astro-ph/0003227 | 1,687,742 | 2,000 | 3 | 15 | true | false | 1 | MISSION |
However, rather than proceeding with a plain fit of a "ad hoc"number of black bodies, we have preferred to use an inversion method to analize the SEDs of the galaxies in the sample. This has the advantage that no assumptions have to be made as to the number or location of the sources responsible for the observed spectr... | 1,558 | astro-ph/0003349 | 1,696,596 | 2,000 | 3 | 23 | true | false | 1 | LAW |
In conclusion, though Kerr's metric for rotating black holes is rightly celebrated as one of the landmark discoveries of 20th century science, the subsequent failure to satisfactorily unite the classical theory of general relativity with quantum mechanics remains a severe impediment to an understanding of nature. Until... | 1,005 | astro-ph/0004051 | 1,708,991 | 2,000 | 4 | 4 | true | false | 1 | UNITS |
- $3 \frac{1}{2}$ decades in energy reach would explore more than 20% of the log-energy gap from our current experimental reach all the way up to the Planck mass scale, at $10^{19}$ GeV. The Planck scale is defined by where quantum gravitational effects necessarily become important enough that even the framework for ou... | 674 | hep-ex/0005008 | 1,740,198 | 2,000 | 5 | 4 | false | true | 2 | UNITS, UNITS |
On ${\cal H}_G$ we introduce multiplication and derivative operators on the dense domain ${\cal D}:=C^\infty(G)$ by FORMULA where $h_{AB}$ denote the matrix elements of the defining representation of $G$ and $i,j,k,..=1,2,..,\dim(G)$ and $X_j(h)=\mbox{tr}([\tau_j h]^T\partial/\partial h)$ denotes the generator of right... | 1,133 | hep-th/0005235 | 1,765,436 | 2,000 | 5 | 25 | false | true | 1 | CONSTANT |
The implementation of a Planck-scale high frequency and short wavelength cutoff in quantum theories on expanding backgrounds may have potentially nontrivial implications, such as the breaking of local Lorentz invariance and the existence of a yet unknown mechanism for the creation of vacuum modes. In scenarios where in... | 901 | astro-ph/0005533 | 1,765,995 | 2,000 | 5 | 26 | true | true | 1 | UNITS |
In the shaded area of Fig. REF (left plot) magnetic fields are produced with growing frequency spectrum. In the shaded area of the right plot of Fig. REF magnetic fields are produced with decreasing frequency spectrum. The theoretical bias would point, a priori, towards increasing frequency spectra. In fact in this cas... | 1,068 | hep-ph/0007163 | 1,820,295 | 2,000 | 7 | 15 | true | true | 2 | UNITS, UNITS |
Therefore, in the context of the standard model extension of Kostelecký and co-workers [CIT], our ${}^{129}$Xe/${}^{3}$He maser measurement improves the constraint on $\tilde{b}^n_J$ to nearly $10^{-31}$ GeV, or more than six times better than the ${}^{199}$Hg/${}^{133}$Cs clock comparison [CIT]. Note that the ratio of... | 812 | physics/0007063 | 1,825,194 | 2,000 | 7 | 18 | false | true | 2 | UNITS, UNITS |
The purpose of this article is to discuss the transition from the Planck epoch to the period when classical gravity prevailed. Some qualitative statements can be made but we will mostly be concerned with defining an order parameter to probe this region and with making estimates about its behavior to determine whether a... | 407 | gr-qc/0007054 | 1,829,308 | 2,000 | 7 | 21 | false | true | 1 | EPOCH |
In the case of strong X-ray irradiation ($\Gamma =1000$) the surface layer is significantly hotter than the disk (Fig. 8, right panel). Temperature inversion is stronger for larger incident angles. As the Planck function of the temperature-inversion layer is greater than the Planck function of the disk where the optica... | 373 | astro-ph/0008016 | 1,841,599 | 2,000 | 8 | 1 | true | false | 2 | LAW, LAW |
The answer to this essential question is in principle in the affirmative, since the pre-Big Bang scenario incorporates a dilaton field coupled to the metric, which modifies the evolution of tensor perturbations. It is well known, indeed, that the transition from an inflationary period to the FRW radiation-dominated era... | 1,501 | hep-th/0010085 | 1,921,169 | 2,000 | 10 | 11 | false | true | 2 | EPOCH, UNITS |
The cosmological constant was introduced by Einstein in 1917 to make the universe static, since it appeared at that time that the universe seemed to be not evolving. But the discovery of the expanding universe in 1929 did not need a static universe, and the cosmological constant has become another parameter in general ... | 956 | hep-th/0011118 | 1,964,655 | 2,000 | 11 | 14 | true | true | 1 | UNITS |
The simulations presented in this paper were carried out on the T3E supercomputer at the Computing Centre of the Max-Planck-Society in Garching, Germany. We are grateful for the hospitality of the Institute for Theoretical Physics at Santa Barbara, where much of the final writing of this paper was completed. | 309 | astro-ph/0012055 | 1,988,473 | 2,000 | 12 | 3 | true | false | 1 | MPS |
One stringent constraint in any cosmological models is nucleosynthesis. It must take place in the conventional radiation dominant era to explain the present amount of light elements. Therefore, $T_c$ must be higher than the temperature at nucleosynthesis, $T_{\rm NS} \sim$ 1 MeV. This constraint implies $m_5 > 1.6 \tim... | 743 | astro-ph/0012313 | 2,004,997 | 2,000 | 12 | 14 | true | true | 1 | UNITS |
We now redefine the field $\hat \phi_i=\sqrt{A\left(L_i\right)}\phi_i$ to absorb the factor $A\left(L_i\right)$ in the kinetic term of the Lagrangian ${\bf L}_i$, so the effective 4-D low energy action becomes FORMULA where $m_{Hi}^2=A(L_i)M_{Hi}^2$ and $m_{ci}^2=A(L_i) M_{ci}^2$. It is important to note that the Newto... | 1,299 | hep-th/0012129 | 2,006,588 | 2,000 | 12 | 14 | true | true | 1 | BRANE |
The first terms here ($\tilde{m}^2$) are the soft ones, which are calculated using the RG equations starting from their values at the GUT (Planck) scale. The second ones are the usual masses of quarks and leptons and the last ones are the $D$ terms of the potential. | 266 | hep-ph/0012288 | 2,016,895 | 2,000 | 12 | 21 | false | true | 1 | UNITS |
[^1]: While it is clear that a truly fundamental role for the Planck length in space-time structure is inconsistent with the combination of the Relativity Principle and ordinary Fitgerald-Lorentz length contraction, it is of course possible [CIT] that the Planck length be associated with some sort of background in a wa... | 1,741 | hep-th/0012238 | 2,021,028 | 2,000 | 12 | 26 | false | true | 5 | UNITS, UNITS, UNITS, UNITS, UNITS |
The observational bound on the cosmological constant is FORMULA where $M_{Pl}$ is the Planck mass (of about $10^{19}$ GeV) and the formula has been written in such a way that the quantity appearing on the left hand side corresponds to the vacuum energy density. This is a very small quantity once one admits the possibli... | 1,694 | hep-th/0012265 | 2,024,496 | 2,000 | 12 | 29 | false | true | 2 | UNITS, UNITS |
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Dataset Card for the Astro-HEP-Planck Corpus
Astro-HEP-Planck Corpus contains 1,494 paragraphs from arXiv papers relating to astrophysics or high energy physics together with word-sense labels for 2,932 occurrences of "Planck".
This table details the main columns of the dataset:
| Column | Description |
|---|---|
| text | Full text of the paragraph |
| length | Number of unicode characters in the paragraph |
| arxiv_id | The arXiv identifier of the paper from which the paragraph was taken |
| text_id | ID of the text/paragraph |
| year | Year of publication of the arXiv paper |
| month | Month of publication of the arXiv paper |
| day | Day of publication of the arXiv paper |
| astro | Whether or not the paper relates to astrophysics |
| hep | Whether or not the paper relates to high energy physics |
| num_planck_labels | Number of labeled occurrences of "Planck" in the paragraph |
| planck_labels | List of word-sense labels for the occurrences of "Planck" in the paragraph |
The primary purpose of the Wikipedia-Physics Corpus lies in its use for analyzing the meaning of concepts in physics. For further insights into the corpus and the underlying research project (Network Epistemology in Practice) please refer to this paper:
Construction
The paragraphs were randomly sampled from the subset of paragraphs in the Astro-HEP Corpus containing the term "Planck".
Occurrences of "Planck" were identified using a case-insensitive regular expression to capture variations like "PLANCK" and "Planck(2015)"" while excluding forms like "planckian". The labels denote distinct meanings of the target term, such as PERSON, CONSTANT, UNITS, LAW, MPS, MISSION, and FOKKER.
Details
- Developer: Arno Simons
- Funded by: The European Union under Grant agreement ID: 101044932
- Language: English
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