Phys. Rev. D 48, 2587–2590 (1993)Scalar field equation in the presence of signature changeReceived 1 March 1993; published in the issue dated 15 September 1993 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. © 1993 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevD.48.2587
DOI:
10.1103/PhysRevD.48.2587
PACS:
04.20.Cv, 02.40.Hw
See AlsoComment: Sean A. Hayward, Comment on ‘‘Failure of standard conservation laws at a classical change of signature’’, Phys. Rev. D 52, 7331 (1995). |
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