Topology Change and the Propagation of Massless Fields

Abstract

We analyse the massless wave equation on a class of two dimensional manifolds consisting of an arbitrary number of topological cylinders connected to one or more topological spheres. Such manifolds are endowed with a degenerate (non-globally hyperbolic) metric. Attention is drawn to the topological constraints on solutions describing monochromatic modes on both compact and non-compact manifolds. Energy and momentum currents are constructed and a new global sum rule discussed. The results offer a rigorous background for the formulation of a field theory of topologically induced particle production.

To appear in J Math Phys. 33 Pages, plain TeX, 5 Postscript figures.

References in corpus (2)

• The Scalar Field Equation in the Presence of Signature Change
• On Cosmological Isotropy, Quantum Cosmology and the Weyl Curvature Hypothesis

Cited by in corpus (6)

• Classical and Quantum Implications of the Causality Structure of Two-Dimensional Spacetimes with Degenerate Metrics
• Casimir effect in a two dimensional signature changing spacetime
• Casimir stress on parallel plates in de Sitter space with signature change
• Casimir effect for a spherical shell in de Sitter spacetime with signature change
• Diffeomorphism algebra of two dimensional free massless scalar field with signature change
• Casimir effect for concentric spheres in de Sitter spacetime with signature change