Classical and Quantum Implications of the Causality Structure of Two-Dimensional Spacetimes with Degenerate Metrics

Abstract

The causality structure of two-dimensional manifolds with degenerate metrics is analysed in terms of global solutions of the massless wave equation. Certain novel features emerge. Despite the absence of a traditional Lorentzian Cauchy surface on manifolds with a Euclidean domain it is possible to uniquely determine a global solution (if it exists), satisfying well defined matching conditions at the degeneracy curve, from Cauchy data on certain spacelike curves in the Lorentzian region. In general, however, no global solution satisfying such matching conditions will be consistent with this data. Attention is drawn to a number of obstructions that arise prohibiting the construction of a bounded operator connecting asymptotic single particle states. The implications of these results for the existence of a unitary quantum field theory are discussed.

27 pages LaTex (6 Figures), Journal of Mathematical Physics (Accepted)

References in corpus (4)

• The Scalar Field Equation in the Presence of Signature Change
• Initial Value Problems and Signature Change
• A Spinor Model for Quantum Cosmology
• Topology Change and the Propagation of Massless Fields

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• Canonical aspects of pregeometric vector-based first order gauge theory
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• Diffeomorphism algebra of two dimensional free massless scalar field with signature change
• Casimir effect for concentric spheres in de Sitter spacetime with signature change