共查询到20条相似文献,搜索用时 31 毫秒
1.
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
2.
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
3.
A locally finite, causal, and quantal substitute for a locally Minkowskian principal fiber bundle
of modules of Cartan differential forms over a bounded region X of a curved C
-smooth spacetime manifold M with structure group G that of orthochronous Lorentz transformations L
+ := SO(1,3), is presented.
is usually regarded as the kinematical structure of classical Lorentzian gravity when the latter is viewed as a Yang-Mills type of gauge theory of a sl(2, {})-valued connection 1-form
. The mathematical structure employed to model this replacement of
is a principal finitary spacetime sheaf
of quantum causal sets
with structure group G
n, which is a finitary version of the continuous group G of local symmetries of General Relativity, and a finitary Lie algebra g
n-valued connection 1-form
on it, which is a section of its subsheaf
.
is physically interpreted as the dynamical field of a locally finite quantum causality, whereas its associated curvature
as some sort of finitary and causal Lorentzian quantum gravity. 相似文献
4.
Given a simple, simply laced, complex Lie algebra
corresponding to the Lie group G, let
be thesubalgebra generated by the positive roots. In this Letter we construct aBV algebra
whose underlying graded commutative algebra is given by the cohomology, with respect to
, of the algebra of regular functions on G with values in
. We conjecture that
describes the algebra of allphysical (i.e., BRST invariant) operators of the noncritical
string. The conjecture is verified in the two explicitly known cases,
2 (the Virasoro string) and
3 (the
string). 相似文献
5.
A general class of Lorentzian metrics,
,
, with
any Riemannian manifold, is introduced in order to generalize classical exact plane fronted waves. Here, we start a systematic study of their main geodesic properties: geodesic completeness, geodesic connectedness and multiplicity causal character of connecting geodesics. These results are independent of the possibility of a full integration of geodesic equations. Variational and geometrical techniques are applied systematically. In particular, we prove that the asymptotic behavior of H(x,u) with x at infinity determines many properties of geodesics. Essentially, a subquadratic growth of H ensures geodesic completeness and connectedness, while the critical situation appears when H(x,u) behaves in some direction as
, as in the classical model of exact gravitational waves. 相似文献
6.
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
7.
Given a braided vector space
, we show that iterated integrals of operator-valued functions satisfying a certain exchange relation give rise to representations of the quantum shuffle algebra built on
. Using the quantum shuffle construction of the 'upper triangular part'
of a quantum shuffle, this provides a simple proof of the result of Bouwknegt, MacCarthy and Pilch saying that integrals of vertex operators acting on certain Fock modules give rise to representations of
. 相似文献
8.
The fusion rules for the (p,q)-minimal model representations of the Virasoro algebra are shown to come from the group
in the following manner. There is a partition
into disjoint subsets and a bijection between
and the sectors
of the (p,q)-minimal model such that the fusion rules
correspond to
where
. 相似文献
9.
In analogy to the KP theory, the second Poisson structure for the dispersionless KP hierarchy can be defined on the space of commutative pseudodifferential operators
. The reduction of the Poisson structure to the symplectic submanifold
gives rise to W-algebras. In this Letter, we discuss properties of this Poisson structure, its Miura transformation and reductions. We are particularly interested in the following two cases: (a) L is pure polynomial in p with multiple roots and (b) L has multiple poles at finite distance. The w-algebra corresponding to the case (a) is defined as
, where
means the multiplicity of roots and to the case (b) is defined by
where
is the multiplicity of poles. We prove that
-algebra is isomorphic via a transformation to
U(1) with m=
. We also give the explicit free fields representations for these W-algebras. 相似文献
10.
The spaces of linear differential operators
acting on -densities on
and the space
of functions on
which are polynomial on the fibers are not isomorphic as modules over the Lie algebra Vect (n) of vector fields of n. However, these modules are isomorphic as sl(n + 1,)-modules where
is the Lie algebra of infinitesimal projective transformations. In addition, such an
-equivariant bijection is unique (up to normalization). This leads to a notion of projectively equivariant quantization and symbol calculus for a manifold endowed with a (flat) projective structure. We apply the
-equivariant symbol map to study the
of kth-order linear differential operators acting on -densities, for an arbitrary manifold M and classify the quotient-modules
. 相似文献
11.
Coupled-state calculations including positronium channels are reported for positron scattering by atomic hydrogen, lithium and sodium. Integrated cross sections and total cross sections are presented for all three atoms. For lithium differential cross sections are also given. Throughout, comparison is made between results calculated with and without inclusion of the positronium channels. S-wave cross sections for positron scattering by atomic hydrogen in the Ps(1s, 2s, 2p)+H(1s, 2s, 2p) approximation show the high energy resonance first observed by Higgins and Burke in the coupled-static approximation. This resonance has now moved up to 51.05 eV and narrowed in width to 2.92 eV. Other pronounced structure is seen in the S-wave cross sections between 10 and 20 eV; it is tentatively suggested that this structure may be due to the formation of a temporary pseudo-molecular collision complex. Results calculated in the Ps(1s, 2s,
, 2p,
,+H(1s, 2s,
, 2p,
approximation show convergence towards accurate values in the energy region below and in the Ore gap. Contrary to previous work on lithium using only an atomic basis, it is found that coupling to the 3d state of lithium is not so important when positronium channels are included; this is because a mixed basis of atom and positronium states gives a more rapidly convergent approximation than an expansion based on atom states alone. The threshold behaviour of the elastic cross section and the Ps(1s) formation cross section for lithium is investigated. Results in the Ps(1s, 2s, 2p)+Na(3s, 3p) approximation for sodium show good agreement with the total cross section measurements of Kwan et al. 相似文献
12.
J. Donin 《Czechoslovak Journal of Physics》1997,47(11):1115-1122
For
we construct a two parametric
-invariant family of algebras,
, that is a quantization of the function algebra
on the coadjoint representation. Along the parameter t the family gives a quantization of the Lie bracket. This family induces a two parametric
-invariant quantization on the maximal orbits, which includes a quantization of the Kirillov-Kostant-Souriau bracket. Yet we construct a quantum de Rham complex on
. 相似文献
13.
The product of two real spectral triples
and
, the first of which is necessarily even, was defined by A.Connes as
given by
and, in the even-even case, by
. Generically it is assumed that the real structure
obeys the relations
,
,
, where the
-sign table depends on the dimension n modulo 8 of the spectral triple. If both spectral triples obey Connes'
>-sign table, it is seen that their product, defined in the straightforward way above, does not necessarily obey this
-sign table. In this Letter, we propose an alternative definition of the product real structure such that the
-sign table is also satisfied by the product. 相似文献
14.
Let
be von Neumann algebras acting on a Hilbert space
and let
be a common cyclic and separating vector. We say that
have the modular intersection property with respect to
if(1)
-half-sided modular inclusions,(2)
(If (1) holds the strong limit exists.) We show that under these conditions the modular groups of
and
generate a 2-dim. Lie group.This observation is the basis for obtaining group representations of Sl(2,
)/Z
2 generated by modular groups. 相似文献
15.
Stan Gudder 《Foundations of Physics》1999,29(6):877-897
This article begins with a review of the framework of fuzzy probability theory. The basic structure is given by the -effect algebra of effects (fuzzy events)
and the set of probability measures
on a measurable space
. An observable
is defined, where
is the value space of X. It is noted that there exists a one-to-one correspondence between states on
and elements of
and between observables
and -morphisms from
to
. Various combinations of observables are discussed. These include compositions, products, direct products, and mixtures. Fuzzy stochastic processes are introduced and an application to quantum dynamics is considered. Quantum effects are characterized from among a more general class of effects. An alternative definition of a statistical map
is given and it is shown that any statistical map has a unique extension to a statistical operator. Finally, various combinations of statistical maps are discussed and their relationships to the corresponding combinations of observables are derived. 相似文献
16.
We develop a geometrical structure of themanifolds and
associated, respectively, withgauge symmetry and BRST symmetry. Then, we show that
, where
is the group of BRST transformations, is endowed with the structureof a principal fiber bundle over the base manifold. Furthermore, in this geometricalsetup, due to the nilpotency of the BRST operator, weprove that the effective action of a gauge theory is aBRST-exact term up to the classical action. Then, weconclude that the effective action where only the gaugesymmetry is fixed is cohomologically equivalent to the action where the gauge and the BRSTsymmetries are fixed. 相似文献
17.
We show that the affine quantum group
is isomorphic to a bicross-product central extension
of the quantum loop group
by a quantum cocycle
in R-matrix form. 相似文献
18.
Let (M, g) be a pseudo-Riemannian manifold and
the space of densities of degree on M. Denote
the space of differential operators from
to
of order k and S
k
with = – the corresponding space of symbols. We construct (the unique) conformally invariant quantization map
. This result generalizes that of Duval and Ovsienko. 相似文献
19.
Marcus Pivato 《Journal of statistical physics》2003,110(1-2):247-267
If
, and
is a finite (nonabelian) group, then
is a compact group; a multiplicative cellular automaton (MCA) is a continuous transformation
which commutes with all shift maps, and where nearby coordinates are combined using the multiplication operation of
. We characterize when MCA are group endomorphisms of
, and show that MCA on
inherit a natural structure theory from the structure of
. We apply this structure theory to compute the measurable entropy of MCA, and to study convergence of initial measures to Haar measure. 相似文献
20.
V. Gaftoi J. Lopez-Bonilla G. Ovando 《International Journal of Theoretical Physics》1999,38(3):939-943
Weert found a superpotential
for the bounded part of the Maxwelltensor
associatedto the Lienard–Wiechert field. Here we obtain afourth-rank generator
for the superpotential
. 相似文献