Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1996-06-21
J.Math.Phys. 37 (1996) 6018-6032
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
27 pages LaTex (6 Figures), Journal of Mathematical Physics (Accepted)
Scientific paper
10.1063/1.531755
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.
Gratus Jonathan
Tucker Robin W.
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