Spectral functions for generalized piston configurations.

In this work we explore various piston configurations with different types of potentials. We analyze Laplace-type operators P=-g^ij ∇^E_i ∇ ^E_j+V where V is the potential. First we study delta potentials and rectangular potentials as examples of non-smooth potentials and find the spectral zeta functions for these piston configurations on manifolds I x N, where I is an interval and N is a smooth compact Riemannian d-1 dimensional manifold. Then we consider the case of any smooth potential with a compact support and develop a method to find spectral functions by finding the asymptotic behavior of the characteristic function of the eigenvalues for P. By means of the spectral zeta function on these various configurations, we obtain the Casimir force and the one-loop effective action for these systems as the values at s= -½ and the derivative at s = 0. Information about the heat kernel coefficients can also be found in the spectral zeta function in the form of residues, which provide an indirect way of finding this geometric information about the manifold and the operator.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Doctoral

Grantor

Baylor University.

Year dc:date.issued

2012

Author dc:creator

• Morales-Almazán, Pedro Fernando.

Advisor dc:contributor.advisor

• Kirsten, Klaus, 1962-

• Spectral functions.
• Casimir effect.

Statement dc:rights

• Baylor University works are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact libraryquestions@baylor.edu for inquiries about permission.

Language dc:language.iso

en

Handle dc:identifier.uri

https://hdl.handle.net/2104/8503

OAI identifier oai:identifier

oai:baylor-ir.tdl.org:2104/8503