Scalar field equation in the presence of signature change

Dray, Tevian and Manogue, Corinne A. and Tucker, Robin (1993) Scalar field equation in the presence of signature change. Physical Review D, 48 (6). pp. 2587-2590. ISSN 1550-7998

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We consider the (massless) scalar field on a two-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.

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Journal Article
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Physical Review D
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07 Aug 2015 11:36
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20 Sep 2023 00:45