Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vacuum Energy Induced by an External Magnetic Field in a Curved Space   The asymptotic expansion of the product of an operator raised to an arbitrary
power and an exponential function of this operator is obtained. With the aid of
this expansion, the density of vacuum energy induced by a static external
magnetic field of an Abelian or non-Abelian nature is expressed in terms of the
DeWitt-Seeley-Gilkey coefficients.

13
The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
3
The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci