• DOI:10.1088/1751-8121/ABC12A
• Corpus ID: 215415971

A new example of the effects of a singular background on the zeta function

@article{Falomir2020ANE,
  title={A new example of the effects of a singular background on the zeta function},
  author={Horacio Falomir and Joaquin Liniado and Pablo A. G. Pisani},
  journal={arXiv: Mathematical Physics},
  year={2020}
}

• H. Falomir, Joaquin Liniado, P. Pisani
• Published 8 April 2020
• Mathematics
• arXiv: Mathematical Physics

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 zeta function does not provide a finite regularization of the effective action. This work extends similar results previously derived in the context of conical singularities.