We present both semiclassical asymptotics for the wave equation on a stationary Kaluza-Klein spacetime and an index theorem describing the difference of the positive-frequency spectral projectors for two stationary regions in a globally hyperbolic spacetime. The first result involves analyzing the restrictions of the wave trace to isotypic subspaces for the action of the structure group, and the asymptotic distribution of the frequencies as the representation corresponding to the isotypic subspace goes to infinity in the weight lattice. For the second result, it was previously known how to calculate the difference of these spectral projectors in the case where they are defined by spacetime regions on which the metric appears ultrastatic. Here we extend these techniques to handle the case where the defining regions merely appear stationary. As such a new formula for the relevant Feynman propagators is derived as one can no longer obtain spectral descriptions of the Feynman propagators of the square of the Dirac operator as is done in the case of local ultrastatic regions.

Creator

• McCormick, Anthony Ryan

DOI

• https://doi.org/10.21985/n2-wq4y-jg28

Subject

• Mathematics

Language

• en

Alternate Identifier

• http://dissertations.umi.com/northwestern:16527
• etdadmin_upload_984183

Keyword

• Kaluza-Klein
• Spacetime
• Quantum
• Spectral
• Index
• Dirac

Date created

• 2023-01-01

Resource type

• Dissertation

Rights statement

• In Copyright