20 research outputs found
Dual Metrics for a Class of Radiative Spacetimes
Second rank non-degenerate Killing tensors for some subclasses of spacetimes
admitting parallel null one-planes are investigated. Lichn\'erowicz radiation
conditions are imposed to provide a physical meaning to spacetimes whose
metrics are described through their associated second rank Killing tensors.
Conditions under which the dual spacetimes retain the same physical properties
are presented.Comment: 8 pages, LaTeX, Minor revisions in the wording in Sec.5. Typo
corrected in references. Journ.-ref adde
The Metric of Yang-Mills Orbit Space on the Lattice
We find coordinates, the metric tensor, the inverse metric tensor and the
Laplace-Beltrami operator for the orbit space of Hamiltonian SU(2) gauge theory
on a finite, rectangular lattice. This is done using a complete axial gauge
fixing. The Gribov problem can be completely solved, with no remaining gauge
ambiguities.Comment: Title is changed in journal. Now 19 pages, still one figure, AMSTe
Jet Bundles in Quantum Field Theory: The BRST-BV method
The geometric interpretation of the Batalin-Vilkovisky antibracket as the
Schouten bracket of functional multivectors is examined in detail. The
identification is achieved by the process of repeated contraction of even
functional multivectors with fermionic functional 1-forms. The classical master
equation may then be considered as a generalisation of the Jacobi identity for
Poisson brackets, and the cohomology of a nilpotent even functional multivector
is identified with the BRST cohomology. As an example, the BRST-BV formulation
of gauge fixing in theories with gauge symmetries is reformulated in the jet
bundle formalism. (Hopefully this version will be TeXable)Comment: 26 page
Poisson brackets with prescribed Casimirs
We consider the problem of constructing Poisson brackets on smooth manifolds
with prescribed Casimir functions. If is of even dimension, we achieve
our construction by considering a suitable almost symplectic structure on ,
while, in the case where is of odd dimension, our objective is achieved by
using a convenient almost cosymplectic structure. Several examples and
applications are presented.Comment: 24 page
Gupta-Bleuler quantization for minimally coupled scalar fields in de Sitter space
We present in this paper a fully covariant quantization of the
minimally-coupled massless field on de Sitter space. We thus obtain a formalism
free of any infrared (e.g logarithmic) divergence. Our method is based on a
rigorous group theoretical approach combined with a suitable adaptation (Krein
spaces) of the Wightman-G\"{a}rding axiomatic for massless fields
(Gupta-Bleuler scheme). We make explicit the correspondence between unitary
irreducible representations of the de Sitter group and the field theory on de
Sitter space-time. The minimally-coupled massless field is associated with a
representation which is the lowest term of the discrete series of unitary
representations of the de Sitter group. In spite of the presence of negative
norm modes in the theory, no negative energy can be measured: expressions as
\le n_{k_1}n_{k_2}...|T_{00}|n_{k_1}n_{k_2}...\re are always positive.Comment: 20 pages, appear in class. quantum gra
Future complete spacetimes with spacelike isometry group and field sources
We extend to the Einstein Maxwell Higgs system results first obtained
previously in collaboration with V. Moncrief for Einstein equations in vacuum.Comment: to appear in proceedings of the greek relativity meeting 200