共查询到20条相似文献,搜索用时 46 毫秒
1.
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
2.
S. L. Woronowicz 《Communications in Mathematical Physics》1972,28(3):221-235
Let
be aC*-algebra and
be an opposite algebra. Notions of exact andj-positive states of
are introduced. It is shown, that any factor state of
can be extended to a pure exactj-positive state
of
. The correspondence
generalizes the notion of the purifications map introduced by Powers and Størmer. The factor states 1 and 2 are quasi-equivalent if and only if their purifications
and
are equivalent. 相似文献
3.
Given a net
of finite-dimensional real Lie algebras contracting into a Lie algebra, a representation
of is constructed explicitly as limit of a net (
l
) of representations, each
l
being a representation of
on a complex Hilbert space
l
. Conditions are imposed on the net (
l
) implying that the carrier space of
contain a-stable set of vectors which are analytic for all, where is a basis of. As a corollary, the corresponding result for contractions of representations of simply connected finite-dimensional real Lie groups is derived.Supported by the Swiss National Science Foundation 相似文献
4.
Yuval Ne'Eman 《General Relativity and Gravitation》1999,31(5):725-735
A superconnection is a supermatrix whose evenpart contains the gaugepotential one-forms of a localgauge group, while the odd parts contain the (zero-form)Higgs fields breaking the local symmetry spontaneously. The combined grading is thus odd everywhere andthe superconnection can be directly derived from aformulation of Noncommutative Geometry, as theappropriate one-form in the relevant form calculus. The simple supergroup
(4, ) (rank = 3) in Kac' classification (evensubgroup
(4,)) provides themost economical spontaneous breaking of
(4,) as gauge group leaving just local
(1,3) unbroken. Post-Riemannian SKY gravity thereby yields Einstein's theory asa low-energy (longer range) effective theory. The theoryis renormalizable and may be unitary. 相似文献
5.
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
6.
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
7.
We show that the Ashtekar-Isham extension
of the configuration space of Yang-Mills theories
is (topologically and measure-theoretically) the projective limit of a family of finite dimensional spaces associated with arbitrary finite lattices.These results are then used to prove that
is contained in a zero measure subset of
with respect to the diffeomorphism invariant Ashtekar-Lewandowski measure on
. Much as in scalar field theory, this implies that states in the quantum theory associated with this measure can be realized as functions on the extended configuration space
. 相似文献
8.
Matthew M. Seabaugh Ender Suvaci Bhaskar Brahmaroutu Gary L. Messing 《Interface Science》2000,8(2-3):257-267
Single crystals of -alumina with {0001}, {11
and {01
2} orientations were embedded in a matrix of liquid phase sintered alumina to study -alumina single crystal growth in the presence of a calcium aluminosilicate liquid. Growth on the {11
0} and {01
2} surfaces was observed to occur by a diffusion-controlled mechanism while growth on the basal surface was controlled by two-dimensional nucleation. Growth models, which incorporate the change in matrix grain size, were derived and shown to fit the growth kinetics. 相似文献
9.
We prove some existence and uniqueness theorems for the solution of the Lichnerowicz equation:
, on an asymptotically Euclidian manifold. This equation governs the conformai factor of a metric solution of the constraints in General Relativity. In the first part we prove existence and uniqueness under the simple assumptionR0,M0,Q0, 0, which insures the monotony of the non-differentiated part. In the second part we obtain an existence theorem under more general hypothesis on the coefficients, by use of the Leray-Schauder degree theory. The results of this paper have been announced in [4]. 相似文献
10.
Varsha Daftardar-Gejji 《General Relativity and Gravitation》1998,30(5):695-700
Brinkmann has shown that conformally related Einstein spaces are either Ricci flat pp-waves or conformally flat spaces with one as de Sitter space and the other being flat. We herewith show that if gikand
are distinct metrics for which
, then both represent (generalised) pp-waves; and w,iis a homothetic conformal Killing vector of gik. It is further observed that in the situation
we can have many (and also non-conformally flat) conformally related solutions, unlike in Einstein spaces. In particular for perfect fluid coupling, we show that the conformally related solutions have to be Friedman-Robertson-Walker metrics with equation of state as
, or pp-waves depending on whether w,iis timelike, spacelike or null. 相似文献
11.
Hans -Jürgen Seifert 《General Relativity and Gravitation》1971,1(3):247-259
A definition of a causal boundary
is given by assigning a future and a past endpoint to any non-extensible timelike or null line. A topology and a partial ordering can be introduced on
. The usual conditions for the causal structure can be formulated as properties of
. This boundary is compared with other types of boundaries.Read on 15 May 1970 at the Gwatt Seminar on the Bearings of Topology upon General RelativityWork supported by the Deutsche Forschungsgemeinschaft. 相似文献
12.
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
13.
We consider Kontsevich star products on the duals of Lie algebras. Such a star product is relative if, for any Lie algebra, its restriction to invariant polynomial functions is the usual pointwise product. Let
be a fixed Lie algebra. We shall say that a Kontsevich star product is
-relative if, on
*, its restriction to invariant polynomial functions is the usual pointwise product. We prove that, if
is a semi-simple Lie algebra, the only strict Kontsevich
-relative star products are the relative (for every Lie algebras) Kontsevich star products. 相似文献
14.
The authors deal with the tunneling of electrons across an inhomogeneous delta-barrier defined by the potential energy
(where
0$$
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and
0$$
" align="middle" border="0">
are two constants). In particular, the perpendicular incidence of an electron with a given value
of the wave vector
is considered. The electron is forward-scattered into the region behind the barrier (region 2:
0$$
" align="middle" border="0">
), i. e. the wave function
is composed of plane waves with all wave vectors
such that
and
\left. 0 \right)} $$
" align="middle" border="0">
) (where
). Therefore, if
0$$
" align="middle" border="0">
, the wave function of the electron is represented as
, where
. An approximate formula is derived for the amplitude
. The authors pay a special attention to the flow density
and calculate this function in two cases: 1. for the plane
and 2. for high values of
is the diffraction angle). The authors discuss the relevance of their diffraction problem in a prospective quantum-mechanical theory of the tunneling of electrons across a randomly inhomogeneous Schottky barrier. 相似文献
15.
L. Burakovsky 《Foundations of Physics》1998,28(10):1595-1605
We show that linear Regge trajectories for mesons and glueballs, and the cubic mass spectrum associated with them, determine a relation between the masses of the meson and the scalar glueball,
, which implies
MeV. We also discuss relations between the masses of the scalar, tensor and 3-- glueballs,
, which imply
MeV. 相似文献
16.
G. Lessner 《General Relativity and Gravitation》1976,7(10):781-803
On the basis of an approximation method developed in a previous paper the motion of an extended small mass on a gravitational background
is investigated. The mass is described by a spherically symmetric rest mass distribution with some form of rigidity; the smallness of the mass is defined by the assumption that the radius of the mass is small compared with the change of the background
. The equation of motion is yielded by integrating Einstein's conservation law of energy and momentum over the world tube of the mass. In the lowest mixed order (mixed of the background
and the retarded potentials of the mass in lowest order) this equation is identical with the geodesic line linearized in
. In the case when the motion on a static background generated by a localized matter distribution is finite, the gravitational radiation of the mass in lowest order is given. 相似文献
17.
The universal R-matrix for a class of esoteric (nonstandard) quantum groups
q(gl(2N+1)) is constructed as a twisting of the universal R-matrix
S of the Drinfeld–Nimbo quantum algebras. The main part of the twisting cocycle
is chosen to be the canonical element of an appropriate pair of separated Hopf subalgebras (quantized Borel's
(N)
q (gl(2N+1))), providing the factorization property of
. As a result, the esoteric quantum group generators can be expressed in terms of Drinfeld and Jimbo. 相似文献
18.
C. Quesne 《International Journal of Theoretical Physics》1999,38(7):1905-1923
GLh(n) ×GLh(m)-covariant (hh)-bosonic[or (hh)-fermionic] algebras
are built in terms of thecorresponding Rh and
-matrices by contracting theGLq(n) ×
-covariant q-bosonic (or q-fermionic) algebras
, = 1, 2.When using a basis of
wherein theannihilation operators are contragredient to thecreation ones, this contraction procedure can be carried out for any n, m values. Whenemploying instead a basis wherein the annihilationoperators, like the creation ones, are irreducibletensor operators with respect to the dual quantumalgebra Uq(gl(n))
, a contraction limit only exists forn, m {1, 2, 4, 6, . . .}. For n = 2, m = 1, andn = m = 2, the resulting relations can be expressed interms of coupled (anti)commutators (as in the classical case), by usingUh(sl(2)) [instead of s1(2)] Clebsch-Gordancoefficients. Some Uh(sl(2)) rank-1/2irreducible tensor operators recently constructed byAizawa are shown to provide a realization of
(2, 1). 相似文献
19.
Within the general framework ofC*-algebra approach to mathematical foundation of statistical mechanics, we prove a theorem which gives a natural explanation for the appearance of the chemical potential (as a thermodynamical parameter labelling equilibrium states) in the presence of a symmetry (under gauge transformations of the first kind). As a symmetry, we consider a compact abelian groupG acting as *-automorphisms of aC*-algebra
(quasi-local field algebra) and commuting (elementwise) with the time translation automorphisms
t
of
. Under a technical assumption which is satisfied by examples of physical interest, we prove that the set of all extremal
t
-KMS states (pure phases) ofG-fixed-point subalgebra
(quasi-local observable algebra) of
satisfying a certain faithfulness condition is in one-to-one correspondence with the set of all extremalG-invariant
t
·
t
-KMS states – of
with varying over one-parameter subgroups ofG (the specification of being the specification of the chemical potential), where the correspondence is that the restriction of – to
is . 相似文献
20.
Horng-Tzer Yau 《Communications in Mathematical Physics》1996,181(2):367-408
Let
denote the grand canonical Gibbs measure of a lattice gas in a cube of sizeL with the chemical potential and a fixed boundary condition. Let
be the corresponding canonical measure defined by conditioning
on
. Consider the lattice gas dynamics for which each particle performs random walk with rates depending on near-by particles. The rates are chosen such that, for everyn andL fixed,
is a reversible measure. Suppose that the Dobrushin-Shlosman mixing conditions holds for
forall chemical potentials . We prove that
for any probability densityf with respect to
; here the constant is independent ofn orL andD denotes the Dirichlet form of the dynamics. The dependence onL is optimal.Research partially supported by U.S. National Science Foundations grant 9403462, Sloan Foundation Fellowship and David and Lucile Packard Foundation Fellowship. 相似文献