共查询到20条相似文献,搜索用时 31 毫秒
1.
Toshiharu Kawai 《General Relativity and Gravitation》1986,18(10):995-1018
We develop a gauge theory of gravity on the basis of the principal fiber bundle over the four-dimensional space-timeM with the covering groupP¯
0
of the proper orthochronous Poincaré group. The field components
are constructed with the connection coefficients
,
and with a Higgs-type field. A Lorentz metricg is introduced with
, which are then identified with the components of duals of the Vierbein fields. Associated with there is a spinor structure onM. For Lagrangian densityL, which is a function of
,
,, matter field , and oftheir first derivatives, we give the conditions imposed by the requirement of the
gauge invariance. The Lagrangian densityL is restricted to be of the formL =L
tot
(, T
klm
,R
klmn
,
k
, ), in whichT
klm
,R
klmn
are the field strengths of
,
, respectively. Identities and conservation laws following from the
gauge invariance are given. Particularly noteworthy is the fact that the energy momentum conservation law follows from theinternal translational invariance. The field equation of is automatically satisfied, if those of
and of are both satisfied. The possible existence of matter fields with intrinsic energy momentum is pointed out. When is a field with vanishing intrinsic energy momentum, the present theory practically agrees with the conventional Poincaré gauge theory of gravity, except for the seemingly trivial terms in the expression of the spin-angular momentum density. A condition leading to a Riemann-Cartan space-time is given. The field holds a key position in the formulation. 相似文献
2.
Christian Kassel 《Communications in Mathematical Physics》1992,146(2):343-356
We show how methods from cyclic homology give easily an explicit 2-cocycle on the Lie algebra of differential operators of the circle such that restricts to the cocycle defining the Virasoro algebra. The same methods yield also aq-analogue of as well as an infinite family of linearly independent cocycles arising when the complex parameterq is a root of unity. We use an algebra ofq-difference operators andq-analogues of Koszul and the Rham complexes to construct these quantum cocycles. 相似文献
3.
Garry Ludwig 《General Relativity and Gravitation》1987,19(1):1-21
Complex Lorentz transformations and complex conformal rescalings with independent conformal factors and
are investigated in terms of elements of the group GL(2,C) G
(2,C). It is shown how a general element of this group decomposes into a standard conformal rescaling (with
=), a pure spin transformation, complex null rotations, and a complex boost-rotation. Of particular interest are the pure spin transformations that leave invariant the metric but transform the permutation spinors. It is these transformations that, when
, are responsible for seemingly complicating the transformation law of the derivative operator and of spinors dependent thereon. It has been suggested that to avoid this complication one should allow the rescaled metric to have torsion. It is argued here that simplicity can be achieved even when the torsion-free condition is imposed. 相似文献
4.
Couch and Torrence suggest that the vacuum Einstein equations admit a larger class of asymptotically flat solutions than those exhibiting the peeling property. Starting with the assumption that
, (d/dr)
and (/x
A
)
, wherex
A
(A = 2, 3) are angular coordinates, they show that
, where 1 2 and 1<0;
, where 2 1 and 1< 1; and 4 and 3 peel as they would under the stronger peeling conditions. The Winicour-Tamburino energy-momentun and angular momentum integrals for these solutions, in general, diverge. In fact, since Couch and Torrence determine only the radial dependence of the solution, it is not clear that the solutions are well defined. We find that the stronger assumption
, (d/dr)
, and (/x
A
)
does result in well-defined solutions for which both the energy-momentum and angular momentum intergrals are not only finite but result in the same expressions as are obtained for peeling space-times. This assumption appears to be the minimal assumption that is necessary for investigating outgoing radiation at null infinity.In part based on a dissertation by Stephanie Novak and submitted to Syracuse University in partial fulfillment of the requirement for the Ph.D. degree. 相似文献
5.
D. Kastler M. Mebkhout G. Loupias L. Michel 《Communications in Mathematical Physics》1972,27(3):195-222
With
aC*-algebra with unit andgG
g
a homomorphic map of a groupG into the automorphism group ofG, the central measure
of a state of
is invariant under the action ofG (in the state space of
) iff is -invariant. Furthermore if the pair {
,G} is asymptotically abelian, is ergodic iff
is ergodic. Transitive ergodic states (corresponding to transitive central measures) are centrally decomposed into primary states whose isotropy groups form a conjugacy class of subgroups. IfG is locally compact and acts continuously on
, the associated covariant representations of {
, } are those induced by such subgroups. Transitive states under time-translations must be primary if required to be stable. The last section offers a complete classification of the isotropy groups of the primary states occurring in the central decomposition of euclidean transitive ergodic invariant states. 相似文献
6.
On the Ricci Curvature of Compact Spacelike Hypersurfaces in Einstein Conformally Stationary-Closed Spacetimes 总被引:1,自引:0,他引:1
In this paper we develop an integral formula involving the Ricci and scalar curvatures of a compact spacelike hypersurface M in a spacetime
equipped with a timelike closed conformal vector field K (in short, conformally stationary-closed spacetime), and we apply it, when
is Einstein, in order to establish sufficient conditions for M to be a leaf of the foliation determined by K and to obtain some non-existence results. We also get some interesting consequences for the particular case when
is a generalized Robertson-Walker spacetime. 相似文献
7.
Atsushi Matsuo 《Communications in Mathematical Physics》1994,160(1):33-48
Theq-vertex operators of Frenkel and Reshetikhin are studied by means of aq-deformation of the Wakimoto module for the quantum affine algebraU
q
at an arbitrary levelk0, –2. A Fock-module version of theq-deformed primary field of spinj is introduced, as well as the screening operators which (anti-)commute with the action ofU
q
up to a total difference of a field. A proof of the intertwining property is given for theq-vertex operators corresponding to the primary fields of spinj1/2Z
0. A sample calculation of the correlation function is also given.This is a revised version of the preprint distributed in December, 1992, with the title Free Field Realization ofq-deformed Primary Fields forU
q
(sl
2) 相似文献
8.
R. P. A. C. Newman 《General Relativity and Gravitation》1981,13(3):257-282
Results are established concerning perturbations of each empty Robertson-Walker space-time (M, g) with a nonvanishing cosmological constant. The perturbed space-times have the general form (
) with
an extension ofM, and
lying in an open neighborhood of g in a type ofW
m
topology. These results indicate that large classes of such perturbations give rise to space-times which suffer from one of two types of incompleteness. 相似文献
9.
We establish a new Howe duality between a pair of two queer Lie superalgebras (q(m),q(n)). This gives a representation theoretic interpretation of a well-known combinatorial identity for Schur Q-functions. We further establish the equivalence between this new Howe duality and the Schur–Sergeev duality between q(n) and a central extension
of the hyperoctahedral group H
k. We show that the zero-weight space of a q(n)-module with highest weight given by a strict partition of n is an irreducible module over the finite group
parameterized by . We also discuss some consequences of this Howe duality. 相似文献
10.
Quantum uncertainties prevent simultaneous measurement of the expansion factor S(t) and its time derivative
. Consequently the Hubble size
has an inherent uncertainty in the quantum state that describes the semiclassical evolution of the universe. We show that the quantum uncertainty in the Hubble size of the universe is amplified to unacceptably large values in any inflationary process.This essay received an honorable mention from the Gravity Research Foundation, 1986-Ed. 相似文献
11.
V. R. Gavrilov V. N. Melnikov S. T. Abdyrakhmanov 《General Relativity and Gravitation》2004,36(7):1579-1592
We study a spatially flat Friedmann model containing a pressureless perfect fluid (dust) and a scalar field with an unbounded from below potential of the form
, where the parameters W
0 and V
0 are arbitrary and
. The model is integrable and all exact solutions describe the recollapsing universe. The behavior of the model near both initial and final points of evolution is analyzed. The model is consistent with the observational parameters. We single out the exact solution with the present-day values of acceleration parameter q
0=0.5 and dark matter density parameter 0=0.3 describing the evolution within the time approximately equal to 2H
0
–1. 相似文献
12.
Michael G. Mürmann 《Journal of statistical physics》1987,48(3-4):769-788
We study the hydrodynamic behavior of a one-dimensional nearest neighbor gradient system with respect to a positive convex potential . In the hydrodynamic limit the density distribution is shown to evolve according to the nonlinear diffusion equation ,(q)/t= (2/dq2){F([1/1(q)]), with F= –. 相似文献
13.
Given n2, we put r=min
. Let be a compact, C
r
-smooth surface in n which contains the origin. Let further
be a family of measurable subsets of such that
as
. We derive an asymptotic expansion for the discrete spectrum of the Schrödinger operator
in L
2(
n
), where is a positive constant, as
. An analogous result is given also for geometrically induced bound states due to a interaction supported by an infinite planar curve. 相似文献
14.
M. Banai 《Foundations of Physics》1985,15(12):1203-1245
An axiomatic framework for describing general space-time models is presented. Space-time models to which irreducible propositional systems belong as causal logics are quantum (q) theoretically interpretable and their event spaces are Hilbert spaces. Such aq space-time is proposed via a canonical quantization. As a basic assumption, the time t and the radial coordinate r of aq particle satisfy the canonical commutation relation [t,r]=±i
. The two cases will be considered simultaneously. In that case the event space is the Hilbert space L2(3). Unitary symmetries consist of Poincaré-like symmetries (translations, rotations, and inversion) and of gauge-like symmetries. Space inversion implies time inversion. Thisq space-time reveals a confinement phenomenon: Theq particle is confined in an
size region of Minkowski space
at any time. One particle mechanics overq space-time provides mass eigenvalue equations for elementary particles. Prugoveki's stochasticq mechanics andq space-time offer a natural way for introducing and interpreting consistently such aq space-time andq particles existing in it. The mass eigenstates ofq particles generate Prugoveki's extended elementary particles. When
0, these particles shrink to point particles and
is recovered as the classical (c) limit ofq space-time. Conceptual considerations favor the case [t,r]=+i
, and applications in hadron physics give the fit
2/5 fermi/GeV.This paper is a revised version of the author's work, Quantization of Space-time and the Corresponding Quantum Mechanics (Part I), report KFKI-1981-48. 相似文献
15.
Rainer Dick 《General Relativity and Gravitation》2004,36(1):217-224
I reconsider the problem of the Newtonian limit in nonlinear gravity models in the light of recently proposed models
with inverse powers of R. Expansion around a maximally symmetric local background with curvature scalar R
0 > 0 gives the correct Newtonian limit on length scales R
0
–1/2 if the gravitational Lagrangian
satisfies f(R
0)f(R0) 1, and I propose two models with f(R
0) = 0. 相似文献
16.
M. M. Tropper 《Journal of statistical physics》1977,17(6):511-528
The ergodic properties of two stochastic models I and II are investigated. Each model is described by a fieldx(t),t > 0, on the lattice =Z
d,d < . For I,x(t) evolves according to the equations wherex
s
(t) R for eachs eF. Here the {ws(t): s } are independent, one-dimensional Wiener processes, 2 is a bounded interaction between adjacent lattice sites, and the potentials 1 and 2 satisfy appropriate regularity conditions. It is shown that for each model,x(t) is a Markov process on an infinite-dimensional phase spaceX. The probability measures onX that satisfy the Dobrushin-Lanford-Ruelle (DLR) conditions are stationary for this process and have a mixing property. Moreover, for I any stationary, time-reversal-invariant probability measure that has certain regularity properties must satisfy the DLR conditions.This paper is based on a portion of the author's Ph.D. thesis.(2) 相似文献
17.
We argue that the Lagrangian for gravity should remain bounded at large curvature, and interpolate between the weak-field tested Einstein-Hilbert Lagrangian EH = R/16G and a pure cosmological constant for large R with the
ansatz cs = EH/
, where l is a length parameter expected to be a few orders of magnitude above the Planck length. The curvature-dependent effective gravitational constant defined by d/dR = 1/16G
eff is G
eff = G
, and tends to infinity for large R, in contrast to most other approaches where G
eff 0. The theory possesses neither ghosts nor tachyons, but it fails to be linearization stable. In a curvature saturated cosmology, the coordinates with ds
2 = a
2 [da
2/B(a) – dx
2 – dy
2 – dz
2] are most convenient since the curvature scalar becomes a linear function of B(a). Cosmological solutions with a singularity of type R ± are possible which have a bounded energy-momentum tensor everywhere; such a behaviour is excluded in Einstein's theory. In synchronized time, the metric is given by
On the technical side we show that two different conformal transformations make cs asymptotically equivalent to the Gurovich-ansatz = |R|4/3 on the one hand, and to Einstein's theory with a minimally coupled scalar field with self-interaction on the other. 相似文献
18.
Ground-state masses ofq
2
–2 states (true and mock baryonium) are investigated in the framework of a Bethe-Salpeter formalism motivated from QCD. The four-particle system is described by pairwise interactions betweenqq orq
pairs with a spectator approximation for the non-interacting pair. The quark-quark interactions are Coulomb plus harmonic interactions; the harmonic terms have been modified to produce linear confinement for heavier quarks, in agreement with experimental spectra. The confining interaction is proportional to the strong coupling constant
s. Apart from the quark masses, the confining interaction is characterized by three basic parameters: (i) a universal spring constant
0; (ii) a constantC
0/
0
2
, which defines the vacuum structure; (iii) a constantA
0, which provides a smooth transition from quadratic to linear confinement as one goes from light to heavy quark systems. These three constants [
0 = 0.158 GeV;C
0=0.296;A
0=0.0283] have been shown to produce excellent fits to all quarkonia states [q
,q
,Q
] as well as baryon spectra (qqq); thus our predictions forq
2
2 states contain no free parameters. In this model, theL=0 ground states occur in the range 1.8–2 GeV, 2.15–2.3 GeV and 6.72–6.75 GeV foru
2
2,s
2
2 andc
2
2 states, respectively. We discuss the prospects for these states to be seen experimentally. In the case of thes
2
2 state, this is likely to have a rather narrow width, and may correspond to theX(2.22 GeV) meson observed in radiative decays of theJ/ meson. Thec
2
2 state might also be visible as a resonance with an appreciable width.Research supported in part by the National Science Foundation under grant NSF-PHY 86-06364Research supported in part by the U.S. Department of Energy 相似文献
19.
Juri Agresti Roberto De Pietri Luca Lusanna Luca Martucci 《General Relativity and Gravitation》2004,36(5):1055-1134
In the framework of the rest-frame instant form of tetrad gravity, where the Hamiltonian is the weak ADM energy
, we define a special completely fixed 3-orthogonal Hamiltonian gauge, corresponding to a choice of non-harmonic 4-coordinates, in which the independent degrees of freedom of the gravitational field are described by two pairs of canonically conjugate Dirac observables (DO)
. We define a Hamiltonian linearization of the theory, i.e. gravitational waves, without
introducing any background 4-metric, by retaining only the linear terms in the DO's in the super-hamiltonian constraint (the Lichnerowicz equation for the conformal factor of the 3-metric) and the quadratic terms in the DO's in
. We solve all the constraints of the linearized theory: this amounts to work in a well defined post-Minkowskian Christodoulou-Klainermann space-time. The Hamilton equations imply the wave equation for the DO's
, which replace the two polarizations of the TT harmonic gauge, and that linearized Einstein's equations are satisfied. Finally we study the geodesic equation, both for time-like and null geodesics, and the geodesic deviation equation. 相似文献
20.
M. A. Oliver 《General Relativity and Gravitation》1977,8(12):975-985
A definition for the energy-momentum tensor of a finite body is given; this utilizes Synge's parallel propagator and an invariant spatial volume element. From the massenergy invariant of the body,
, is obtained. A new interpretation of the constantM in Schwarzschild's exterior solution is given. 相似文献