Some subtleties in the relationships among heat kernel invariants, eigenvalue distributions, and quantum vacuum energy

A common tool in Casimir physics (and many other areas) is the asymptotic (high-frequency) expansion of eigenvalue densities, employed as either input or output of calculations of the asymptotic behavior of various Green functions. Here we clarify some fine points and potentially confusing aspects o...

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Bibliographic Details
Published inJournal of physics. A, Mathematical and theoretical Vol. 48; no. 4; pp. 45402 - 13
Main Authors Fulling, S A, Yang, Yunyun
Format Journal Article
LanguageEnglish
Published IOP Publishing 30.01.2015
Subjects
Asymptotic properties
Density
distributions
Eigenvalues
Functions (mathematics)
Green functions
Invariants
Mathematical analysis
Spectra
spectral asymptotics
vacuum energy
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ISSN1751-8113
1751-8121
DOI10.1088/1751-8113/48/4/045402

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Summary:A common tool in Casimir physics (and many other areas) is the asymptotic (high-frequency) expansion of eigenvalue densities, employed as either input or output of calculations of the asymptotic behavior of various Green functions. Here we clarify some fine points and potentially confusing aspects of the subject. In particular, we show how recent observations of Kolomeisky et al (2013 Phys. Rev. A 87 042519) fit into the established framework of the distributional asymptotics of spectral functions.
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ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/48/4/045402