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General Relativity and Quantum Cosmology

Title: The Scalar Field Equation in the Presence of Signature Change

Abstract: We consider the (massless) scalar field on a 2-dimensional manifold with metric that changes signature from Lorentzian to Euclidean. Requiring a conserved momentum in the spatially homogeneous case leads to a particular choice of propagation rule. The resulting mix of positive and negative frequencies depends only on the total (conformal) size of the spacelike regions and not on the detailed form of the metric. Reformulating the problem using junction conditions, we then show that the solutions obtained above are the unique ones which satisfy the natural distributional wave equation everywhere. We also give a variational approach, obtaining the same results from a natural Lagrangian.
(PACS numbers 04.20.Cv and 02.40.+m.)
Comments: requires REVTeX 2.0 or 3.0 (Plain TeX version available on request), 4 pages by default (12 in preprint style), no figures
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
Journal reference: Phys.Rev. D48 (1993) 2587-2590
DOI: 10.1103/PhysRevD.48.2587
Cite as: arXiv:gr-qc/9303002
  (or arXiv:gr-qc/9303002v1 for this version)

Submission history

From: Tevian Dray [view email]
[v1] Mon, 1 Mar 1993 22:45:16 GMT (9kb)