305 research outputs found
Spacetime torsion and parity violation: a gauge invariant formulation
The possibility of parity violation through spacetime torsion has been
explored in a scenario containing fields with different spins. Taking the
Kalb-Ramond field as the source of torsion, an explicitly parity violating
gauge invariant theory has been constructed by extending the KR
field with a Chern-Simons term.Comment: 4 pages, RevTe
Lagrangian versus Quantization
We discuss examples of systems which can be quantized consistently, although
they do not admit a Lagrangian description.Comment: 8 pages, no figures; small corrections, references adde
Quantization of Nonstandard Hamiltonian Systems
The quantization of classical theories that admit more than one Hamiltonian
description is considered. This is done from a geometrical viewpoint, both at
the quantization level (geometric quantization) and at the level of the
dynamics of the quantum theory. A spin-1/2 system is taken as an example in
which all the steps can be completed. It is shown that the geometry of the
quantum theory imposes restrictions on the physically allowed nonstandard
quantum theories.Comment: Revtex file, 23 pages, no figure
Variations on the Seventh Route to Relativity
As motivated in the full abstract, this paper further investigates Barbour,
Foster and O Murchadha (BFO)'s 3-space formulation of GR. This is based on
best-matched lapse-eliminated actions and gives rise to several theories
including GR and a conformal gravity theory. We study the simplicity postulates
assumed in BFO's work and how to weaken them, so as to permit the inclusion of
the full set of matter fields known to occur in nature.
We study the configuration spaces of gravity-matter systems upon which BFO's
formulation leans. In further developments the lapse-eliminated actions used by
BFO become impractical and require generalization. We circumvent many of these
problems by the equivalent use of lapse-uneliminated actions, which furthermore
permit us to interpret BFO's formulation within Kuchar's generally covariant
hypersurface framework. This viewpoint provides alternative reasons to BFO's as
to why the inclusion of bosonic fields in the 3-space approach gives rise to
minimally-coupled scalar fields, electromagnetism and Yang--Mills theory. This
viewpoint also permits us to quickly exhibit further GR-matter theories
admitted by the 3-space formulation. In particular, we show that the spin-1/2
fermions of the theories of Dirac, Maxwell--Dirac and Yang--Mills--Dirac, all
coupled to GR, are admitted by the generalized 3-space formulation we present.
Thus all the known fundamental matter fields can be accommodated. This
corresponds to being able to pick actions for all these theories which have
less kinematics than suggested by the generally covariant hypersurface
framework. For all these theories, Wheeler's thin sandwich conjecture may be
posed, rendering them timeless in Barbour's sense.Comment: Revtex version; Journal-ref adde
The Husain-Kuchar Model: Time Variables and Non-degenerate Metrics
We study the Husain-Kuchar model by introducing a new action principle
similar to the self-dual action used in the Ashtekar variables approach to
Quantum Gravity. This new action has several interesting features; among them,
the presence of a scalar time variable that allows the definition of geometric
observables without adding new degrees of freedom, the appearance of a natural
non-degenerate four-metric and the possibility of coupling ordinary matter.Comment: LaTeX, 22 pages, accepted for publication in Phys. Rev.
Classification of Spherically Symmetric Static Spacetimes according to their Matter Collineations
The spherically symmetric static spacetimes are classified according to their
matter collineations. These are studied when the energy-momentum tensor is
degenerate and also when it is non-degenerate. We have found a case where the
energy-momentum tensor is degenerate but the group of matter collineations is
finite. For the non-degenerate case, we obtain either {\it four}, {\it five},
{\it six} or {\it ten} independent matter collineations in which four are
isometries and the rest are proper. We conclude that the matter collineations
coincide with the Ricci collineations but the constraint equations are
different which on solving can provide physically interesting cosmological
solutions.Comment: 15 pages, no figure, Late
Interacting vector fields in Relativity without Relativity
Barbour, Foster and \'{O} Murchadha have recently developed a new framework,
called here {\it{the 3-space approach}}, for the formulation of classical
bosonic dynamics. Neither time nor a locally Minkowskian structure of spacetime
are presupposed. Both arise as emergent features of the world from
geodesic-type dynamics on a space of 3-dimensional metric--matter
configurations. In fact gravity, the universal light cone and Abelian gauge
theory minimally coupled to gravity all arise naturally through a single common
mechanism. It yields relativity -- and more -- without presupposing relativity.
This paper completes the recovery of the presently known bosonic sector within
the 3-space approach. We show, for a rather general ansatz, that 3-vector
fields can interact among themselves only as Yang--Mills fields minimally
coupled to gravity.Comment: Replaced with final version accepted by Classical and Quantum Gravity
(14 pages, no figures
Lagrangian approach to a symplectic formalism for singular systems
We develop a Lagrangian approach for constructing a symplectic structure for
singular systems. It gives a simple and unified framework for understanding the
origin of the pathologies that appear in the Dirac-Bergmann formalism, and
offers a more general approach for a symplectic formalism, even when there is
no Hamiltonian in a canonical sense. We can thus overcome the usual limitations
of the canonical quantization, and perform an algebraically consistent
quantization for a more general set of Lagrangian systems.Comment: 30 page
Quantum Field Theory with Null-Fronted Metrics
There is a large class of classical null-fronted metrics in which a free
scalar field has an infinite number of conservation laws. In particular, if the
scalar field is quantized, the number of particles is conserved. However, with
more general null-fronted metrics, field quantization cannot be interpreted in
terms of particle creation and annihilation operators, and the physical meaning
of the theory becomes obscure.Comment: 11 page
Action functionals of single scalar fields and arbitrary--weight gravitational constraints that generate a genuine Lie algebra
We discuss the issue initiated by Kucha\v{r} {\it et al}, of replacing the
usual Hamiltonian constraint by alternative combinations of the gravitational
constraints (scalar densities of arbitrary weight), whose Poisson brackets
strongly vanish and cast the standard constraint-system for vacuum gravity into
a form that generates a true Lie algebra. It is shown that any such
combination---that satisfies certain reality conditions---may be derived from
an action principle involving a single scalar field and a single Lagrange
multiplier with a non--derivative coupling to gravity.Comment: 26 pages, plain TE
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