Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact solutions of the bound Dirac and Klein Gordon equations in non co
  propagating electromagnetic plane waves   A new class of exact solutions of the bound Dirac and bound Klein Gordon
equations in non co propagating plane waves is found. The solutions are based
on the physical principle of maintaining local gauge invariance in the Furry
picture Lagrangian when N external fields can undergo independent gauge
transformations. The solutions can be expressed in terms of the Hamilton Jacobi
action and a gauge invariant effective particle momentum in the ensemble of
external fields. Rotations of the effective particle momentum, which preserve
local gauge invariance, are introduced into the action using matrix calculus.
The set of such rotations provides the class of new solutions constituting a
family of Volkov like solutions for one external field. When applied to two or
more non co propagating external fields, the rotational symmetry provides
counter terms which decouple the fields. The bound state equations of motion
become solvable for any number of non co propagating external fields. Through
angular spectral decomposition, which represents electromagnetic fields of any
form as a spatial Fourier series of non co propagating plane waves, the new
solutions described here can be applied to strong field physics problems in any
external electromagnetic field.

24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess