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Letters in Mathematical Physics

, Volume 105, Issue 4, pp 523–549 | Cite as

QFT Over the Finite Line. Heat Kernel Coefficients, Spectral Zeta Functions and Selfadjoint Extensions

  • Jose M. Muñoz-Castañeda
  • Klaus Kirsten
  • Michael Bordag
Article

Abstract

Following the seminal works of Asorey–Ibort–Marmo and Muñoz–Castañeda–Asorey about selfadjoint extensions and quantum fields in bounded domains, we compute all the heat kernel coefficients for any strongly consistent selfadjoint extension of the Laplace operator over the finite line [0, L]. The derivative of the corresponding spectral zeta function at s = 0 (partition function of the corresponding quantum field theory) is obtained. To compute the correct expression for the a 1/2 heat kernel coefficient, it is necessary to know in detail which non-negative selfadjoint extensions have zero modes and how many of them they have. The answer to this question leads us to analyze zeta function properties for the Von Neumann–Krein extension, the only extension with two zero modes.

Keywords

Quantum Theory Quantum field theory on curved space backgrounds Casimir effect Scattering theory Parameter dependent boundary value problems Boundary value problems for second-order elliptic equations Zeta and L-functions: analytic theory Symmetric and selfadjoint operators General theory of linear operators 

Mathematics Subject Classification

81S99 81T20 81T55 81U99 34B08 35J25 11M36 47B25 47A10 

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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Jose M. Muñoz-Castañeda
    • 1
  • Klaus Kirsten
    • 2
  • Michael Bordag
    • 1
  1. 1.Institut für Theoretische PhysikUniversität LeipzigLeipzigGermany
  2. 2.GCAP-CASPER Department of MathematicsBaylor UniversityWacoUSA

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