A New Example of the Effects of a Singular Background on the Zeta Function

To motivate our discussion, we consider a 1+1 dimensional scalar field interacting with a static Coulomb-type background, so that the spectrum of quantum fluctuations is given by a second-order differential operator on a single coordinate r with a singular coefficient proportional to 1/r. We find th...

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Detalles Bibliográficos
Autores principales: Falomir, Horacio Alberto, Liniado, Joaquín, González Pisani, Pablo Andrés
Formato: Articulo Preprint
Lenguaje:Inglés
Publicado: 2020
Materias:
Física
Scalar field
Effective action
Physics
Gravitational singularity
Operator (physics)
Spectrum (functional analysis)
Complex plane
Riemann zeta function
Mathematical physics
Differential operator
Regularization (physics)
Proper time
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/124581
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-124581
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Física
Scalar field
Effective action
Physics
Gravitational singularity
Operator (physics)
Spectrum (functional analysis)
Complex plane
Riemann zeta function
Mathematical physics
Differential operator
Regularization (physics)
Proper time
spellingShingle Física
Scalar field
Effective action
Physics
Gravitational singularity
Operator (physics)
Spectrum (functional analysis)
Complex plane
Riemann zeta function
Mathematical physics
Differential operator
Regularization (physics)
Proper time
Falomir, Horacio Alberto
Liniado, Joaquín
González Pisani, Pablo Andrés
A New Example of the Effects of a Singular Background on the Zeta Function
topic_facet Física
Scalar field
Effective action
Physics
Gravitational singularity
Operator (physics)
Spectrum (functional analysis)
Complex plane
Riemann zeta function
Mathematical physics
Differential operator
Regularization (physics)
Proper time
description To motivate our discussion, we consider a 1+1 dimensional scalar field interacting with a static Coulomb-type background, so that the spectrum of quantum fluctuations is given by a second-order differential operator on a single coordinate r with a singular coefficient proportional to 1/r. We find that the spectral functions of this operator present an interesting behavior: the zeta function has multiple poles in the complex plane; accordingly, logarithms of the proper time appear in the heat-trace expansion. As a consequence, the ζ function does not provide a finite regularization of the effective action. This work extends similar results previously derived in the context of conical singularities.
format Articulo
Preprint
author Falomir, Horacio Alberto
Liniado, Joaquín
González Pisani, Pablo Andrés
author_facet Falomir, Horacio Alberto
Liniado, Joaquín
González Pisani, Pablo Andrés
author_sort Falomir, Horacio Alberto
title A New Example of the Effects of a Singular Background on the Zeta Function
title_short A New Example of the Effects of a Singular Background on the Zeta Function
title_full A New Example of the Effects of a Singular Background on the Zeta Function
title_fullStr A New Example of the Effects of a Singular Background on the Zeta Function
title_full_unstemmed A New Example of the Effects of a Singular Background on the Zeta Function
title_sort new example of the effects of a singular background on the zeta function
publishDate 2020
url http://sedici.unlp.edu.ar/handle/10915/124581
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bdutipo_str Repositorios
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