Topology Change and the Propagation of Massless Fields

TL;DR

This paper investigates the behavior of massless fields on complex two-dimensional manifolds with changing topology, revealing topological constraints and energy conservation principles relevant for particle production theories.

Contribution

It introduces a rigorous analysis of wave equations on non-globally hyperbolic manifolds with topology change, including energy currents and a new global sum rule.

Findings

Topological constraints affect monochromatic mode solutions.

Energy and momentum currents are explicitly constructed.

A global sum rule for solutions is established.

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.