arXiv subjects

Philip A. Tuckey

Publications and source records attributed to Philip A. Tuckey.

5 recordsLinked to original sources

arXiv1997

Tensor distributions on signature-changing space-times

Irregularities in the metric tensor of a signature-changing space-time suggest that field equations on such space-times might be regarded as distributional. We review the formalism of tensor distributions on differentiable manifolds, and examine to what extent rigorous meaning can be given to field equations in the presence of signature-change, in particular those involving covariant derivatives. We find that, for both continuous and discontinuous signature-change, covariant differentiation can be defined on a class of tensor distributions wide enough to be physically interesting.

gr-qc↗

arXiv1995

On quantum and parallel transport in a Hilbert bundle over spacetime

We study the Hilbert bundle description of stochastic quantum mechanics in curved spacetime developed by Prugovečki, which gives a powerful new framework for exploring the quantum mechanical propagation of states in curved spacetime. We concentrate on the quantum transport law in the bundle, specifically on the information which can be obtained from the flat space limit. We give a detailed proof that quantum transport coincides with parallel transport in the bundle in this limit, confirming statements of Prugovečki. We furthermore show that the quantum-geometric propagator in curved spacetime proposed by Prugovečki, yielding a Feynman path integral-like formula involving integrations over intermediate phase space variables, is Poincaré gauge covariant (i.e.$\!$ is gauge invariant except for transformations at the endpoints of the path) provided the integration measure is interpreted as a ``contact point measure'' in the soldered stochastic phase space bundle raised over curved spacetime.

gr-qc↗

arXiv1994

A Parallelizable Implicit Evolution Scheme for Regge Calculus

The role of Regge calculus as a tool for numerical relativity is discussed, and a parallelizable implicit evolution scheme described. Because of the structure of the Regge equations, it is possible to advance the vertices of a triangulated spacelike hypersurface in isolation, solving at each vertex a purely local system of implicit equations for the new edge-lengths involved. (In particular, equations of global ``elliptic-type'' do not arise.) Consequently, there exists a parallel evolution scheme which divides the vertices into families of non-adjacent elements and advances all the vertices of a family simultaneously. The relation between the structure of the equations of motion and the Bianchi identities is also considered. The method is illustrated by a preliminary application to a 600--cell Friedmann cosmology. The parallelizable evolution algorithm described in this paper should enable Regge calculus to be a viable discretization technique in numerical relativity.

gr-qc↗

arXiv1994

Geometry and Dynamics with Time-Dependent Constraints

We describe how geometrical methods can be applied to a system with explicitly time-dependent second-class constraints so as to cast it in Hamiltonian form on its physical phase space. Examples of particular interest are systems which require time-dependent gauge fixing conditions in order to reduce them to their physical degrees of freedom. To illustrate our results we discuss the gauge-fixing of relativistic particles and strings moving in arbitrary background electromagnetic and antisymmetric tensor fields.

hep-th↗

arXiv1992

A Geometrical Approach to Time-Dependent Gauge-Fixing

When a Hamiltonian system is subject to constraints which depend explicitly on time, difficulties can arise in attempting to reduce the system to its physical phase space. Specifically, it is non-trivial to restrict the system in such a way that one can find a Hamiltonian time-evolution equation involving the Dirac bracket. Using a geometrical formulation, we derive an explicit condition which is both necessary and sufficient for this to be possible, and we give a formula defining the resulting Hamiltonian function. Some previous results are recovered as special cases.

hep-th↗