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Classical and quantum implications of the causality structure of two-dimensional space-times with degenerate metrics

Gratus, Jonathan and Tucker, Robin (1996) Classical and quantum implications of the causality structure of two-dimensional space-times with degenerate metrics. Journal of Mathematical Physics, 37 (12). pp. 6018-6032. ISSN 0022-2488

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Abstract

The causality structure of two-dimensional manifolds with degenerate metrics is analyzed 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.

Item Type: Article
Journal or Publication Title: Journal of Mathematical Physics
Uncontrolled Keywords: SIGNATURE TYPE CHANGE ; GENERAL-RELATIVITY
Subjects:
Departments: Faculty of Science and Technology > Physics
ID Code: 64124
Deposited By: ep_importer_pure
Deposited On: 09 May 2013 15:43
Refereed?: Yes
Published?: Published
Last Modified: 21 Sep 2017 05:35
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/64124

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