1,226 research outputs found
Hamiltonian Analysis of the Conformal Decomposition of the Gravitational Field
This short note is devoted to the Hamiltonian formulation of the conformal
decomposition of the gravitational field that was performed in [gr-qc/0501092].
We also analyze the gauge fixed form of the theory when we fix the conformal
symmetry by imposing the condition det g=1.Comment: 12 page
Hamiltonian Analysis of Non-Relativistic Covariant RFDiff Horava-Lifshitz Gravity
We perform the Hamiltonian analysis of non-relativistic covariant
Horava-Lifshitz gravity in the formulation presented recently in
arXiv:1009.4885. We argue that the resulting Hamiltonian structure is in
agreement with the original construction of non-relativistic covariant
Ho\v{r}ava-Lifshitz gravity presented in arXiv:1007.2410. Then we extend this
construction to the case of RFDiff invariant Ho\v{r}ava-Lifshitz theory. We
find well behaved Hamiltonian system with the number of the first and the
second class constraints that ensure the correct number of physical degrees of
freedom of gravity.Comment: 15 pages, v2. Title changed, major corrections in section 3.
performed, corrected typos and references added,v3: additional typos
corrected, references added,v4.additional comments added, version published
in PR
Gauge Invariance for Generally Covariant Systems
Previous analyses on the gauge invariance of the action for a generally
covariant system are generalized. It is shown that if the action principle is
properly improved, there is as much gauge freedom at the endpoints for an
arbitrary gauge system as there is for a system with ``internal'' gauge
symmetries. The key point is to correctly identify the boundary conditions for
the allowed histories and to include the appropriate end-point contribution in
the action. The path integral is then discussed. It is proved that by employing
the improved action, one can use time-independent canonical gauges even in the
case of generally covariant theories. From the point of view of the action and
the path integral, there is thus no conceptual difference between general
covariance and ``ordinary gauge invariance''. The discussion is illustrated in
the case of the point particle, for which various canonical gauges are
considered.Comment: 41 pages, ULB-PMIF-92-0
Generalized Smarr relation for Kerr AdS black holes from improved surface integrals
By using suitably improved surface integrals, we give a unified geometric
derivation of the generalized Smarr relation for higher dimensional Kerr black
holes which is valid both in flat and in anti-de Sitter backgrounds. The
improvement of the surface integrals, which allows one to use them
simultaneously at infinity and on the horizon, consists in integrating them
along a path in solution space. Path independence of the improved charges is
discussed and explicitly proved for the higher dimensional Kerr AdS black
holes. It is also shown that the charges for these black holes can be correctly
computed from the standard Hamiltonian or Lagrangian surface integrals.Comment: 21 pages Latex file, 1 figure; discussion on integrability rectified,
typo in (2.14) correcte
The local degrees of freedom of higher dimensional pure Chern-Simons theories
The canonical structure of higher dimensional pure Chern-Simons theories is
analysed. It is shown that these theories have generically a non-vanishing
number of local degrees of freedom, even though they are obtained by means of a
topological construction. This number of local degrees of freedom is computed
as a function of the spacetime dimension and the dimension of the gauge group.Comment: 9 pages, RevTeX3.0 (LaTeX2.09), no figure
A Weyl-covariant tensor calculus
On a (pseudo-) Riemannian manifold of dimension n > 2, the space of tensors
which transform covariantly under Weyl rescalings of the metric is built. This
construction is related to a Weyl-covariant operator D whose commutator [D,D]
gives the conformally invariant Weyl tensor plus the Cotton tensor. So-called
generalized connections and their transformation laws under diffeomorphisms and
Weyl rescalings are also derived. These results are obtained by application of
BRST techniques.Comment: LaTeX, 10 pages. Minor corrections and a reference adde
The Maurer-Cartan structure of BRST differential
In this paper, we construct a new sequence of generators of the BRST complex
and reformulate the BRST differential so that it acts on elements of the
complex much like the Maurer-Cartan differential acts on left-invariant forms.
Thus our BRST differential is formally analogous to the differential defined on
the BRST formulation of the Chevalley-Eilenberg cochain complex of a Lie
algebra. Moreover, for an important class of physical theories, we show that in
fact the differential is a Chevalley-Eilenberg differential. As one of the
applications of our formalism, we show that the BRST differential provides a
mechanism which permits us to extend a nonintegrable system of vector fields on
a manifold to an integrable system on an extended manifold
BRST-BFV method for nonstationary systems
Starting from an associated reparametrization-invariant action, the
generalization of the BRST-BFV method for the case of nonstationary systems is
constructed. The extension of the Batalin-Tyutin conversional approach is also
considered in the nonstationary case. In order to illustrate these ideas, the
propagator for the time-dependent two-dimensional rotor is calculated by
reformulating the problem as a system with only first class constraints and
subsequently using the BRST-BFV prescription previously obtained.Comment: Latex, RevTeX, 13 page
A note on BRST quantization of SU(2) Yang-Mills mechanics
The quantization of SU(2) Yang-Mills theory reduced to 0+1 space-time
dimensions is performed in the BRST framework. We show that in the unitary
gauge the BRST procedure has difficulties which can be solved by
introduction of additional singlet ghost variables. In the Lorenz gauge
one has additional unphysical degrees of freedom, but the BRST
quantization is free of the problems in the unitary gauge.Comment: 17 page
On the Strong Homotopy Lie-Rinehart Algebra of a Foliation
It is well known that a foliation F of a smooth manifold M gives rise to a
rich cohomological theory, its characteristic (i.e., leafwise) cohomology.
Characteristic cohomologies of F may be interpreted, to some extent, as
functions on the space P of integral manifolds (of any dimension) of the
characteristic distribution C of F. Similarly, characteristic cohomologies with
local coefficients in the normal bundle TM/C of F may be interpreted as vector
fields on P. In particular, they possess a (graded) Lie bracket and act on
characteristic cohomology H. In this paper, I discuss how both the Lie bracket
and the action on H come from a strong homotopy structure at the level of
cochains. Finally, I show that such a strong homotopy structure is canonical up
to isomorphisms.Comment: 41 pages, v2: almost completely rewritten, title changed; v3:
presentation partly changed after numerous suggestions by Jim Stasheff,
mathematical content unchanged; v4: minor revisions, references added. v5:
(hopefully) final versio
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