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.)

requires REVTeX 2.0 or 3.0 (Plain TeX version available on request), 4 pages by default (12 in preprint style), no figures

References in corpus (2)

• Tensor Distributions in the Presence of Degenerate Metrics
• Scalar and Spinor Fields in Signature Changing Spacetimes

Cited by in corpus (47)

• Complex actions in two-dimensional topology change
• From Euclidean to Lorentzian General Relativity: The Real Way
• Failure of Standard Conservation Laws at a Classical Change of Signature
• Vacuum as a hyperbolic metamaterial
• Signature change events: A challenge for quantum gravity?
• On Singular Semi-Riemannian Manifolds
• Einstein's Equations in the Presence of Signature Change
• Actions for signature change
• Metrics with distributional curvature
• BOUNDARY CONDITIONS FOR THE SCALAR FIELD IN THE PRESENCE OF SIGNATURE CHANGE
• Comment on "Failure of standard conservation laws at a classical change of signature"
• Reply Comment: Comparison of Approaches to Classical Signature Change
• Tensor Distributions in the Presence of Degenerate Metrics
• Cosmological perturbations and classical change of signature
• General solutions of Einstein's spherically symmetric gravitational equations with junction conditions
• Note on Signature Change and Colombeau Theory
• A quantum cosmology and discontinuous signature changing classical solutions
• Square Root Actions, Metric Signature, and the Path-Integral of Quantum Gravity
• The Patchwork Divergence Theorem
• Modeling Kleinian cosmology with electronic metamaterials
• Comment on `Smooth and Discontinuous Signature Type Change in General Relativity'
• Tensor distributions on signature-changing space-times
• Uniqueness of the Fock quantization of scalar fields and processes with signature change in cosmology
• Initial Value Problems and Signature Change
• Riemann-Cartan gravity with dynamical signature
• Singular General Relativity
• Emergent spacetimes
• Interpolating Between Topologies: Casimir Energies
• Piecewise Conserved Quantities
• Classical and Quantum Implications of the Causality Structure of Two-Dimensional Spacetimes with Degenerate Metrics
• On metric-connection compatibility and the signature change of space-time
• Topology Change and the Propagation of Massless Fields
• Alternative route towards the change of metric signature
• Should Metric Signature Matter in Clifford Algebra Formulations of Physical Theories?
• The Construction of Spinor Fields on Manifolds with Smooth Degenerate Metrics
• Obstructions to Pin Structures on Kleinian Manifolds
• Self-adjoint extensions and Signature Change
• Casimir effect in a two dimensional signature changing spacetime
• Isochronous Spacetimes
• Singularity at the demise of a black hole
• Casimir stress on parallel plates in de Sitter space with signature change
• Casimir effect for a spherical shell in de Sitter spacetime with signature change
• The trace left by signature-change-induced compactification
• Isochronous solutions of Einstein's equations and their Newtonian limit
• Diffeomorphism algebra of two dimensional free massless scalar field with signature change
• Casimir effect for concentric spheres in de Sitter spacetime with signature change
• Extra-dimensional metamaterials: simple models of inflation and metric signature transitions