Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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
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.

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The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
18
The categories of this paper are: econ
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The categories of this paper are: comp-gas