Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equivalence of zeta function technique and Abel-Plana formula in
  regularizing the Casimir energy of hyper-rectangular cavities   Zeta function regularization is an effective method to extract physical
significant quantities from infinite ones. It is regarded as mathematically
simple and elegant but the isolation of the physical divergency is hidden in
its analytic continuation. By contrast, Abel-Plana formula method permits
explicit separation of divergent terms. In regularizing the Casimir energy for
a massless scalar field in a $D$-dimensional rectangular box, we give the
rigorous proof of the equivalence of the two methods by deriving the reflection
formula of Epstein zeta function from repeatedly application of Abel-plana
formula and giving the physical interpretation of the infinite integrals. Our
study may help with the confidence of choosing any regularization method at
convenience among the frequently used ones, especially the zeta function
method, without the doubts of physical meanings or mathematical consistency.

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The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th