Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometry Dependence of Casimir Forces beyond the Proximity Approximation   Casimir interactions between macroscopic objects are strongly influenced by
their geometrical features as shape and orientation as well as by their
material properties. The effect of geometry is commonly obtained from the
proximity approximation (PA). Here we present a path integral quantization for
the electromagnetic field in the presence of deformed metallic surfaces. From
the resulting effective action the Casimir force between the surfaces can be
calculated without the PA. For corrugated surfaces the force is obtained both
perturbatively for small deformations and by a numerical approach for general
deformation amplitudes. For general dielectric materials with flat surfaces a
path integral based derivation of the Lifshitz theory is outlined, pointing
towards a possible approach to study the combined effect of deformations and
material properties.

17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
2
The categories of this paper are: math
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc