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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| Autores principales: | , , |
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| Formato: | Articulo Preprint |
| Lenguaje: | Inglés |
| Publicado: |
2020
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| Materias: | |
| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/124581 |
| Aporte de: |
| Sumario: | 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. |
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