Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equivalent sets of solutions of the Klein-Gordon equation with a
  constant electric field   In connection with the problem of choosing the in- and out-states among the
solutions of a wave equation with one-dimensional potential we study
nonstationary and "stationary" families of complete sets. A nonstationary set
consists of the solutions with the quantum number $p_v=p^0v-p_3.$ It can be
obtained from the nonstationary set with quantum number $p_3$ by a boost along
$x_3$-axis (along the direction of the electric field) with velocity $-v$. By
changing the gauge the solutions in all sets can be brought to one and the same
potential without changing quantum numbers. Then the transformations of
solutions of one set (with quantum number $p_v$) to the solutions in another
set (with quantum number $p_{v'}$) have the group properties.
  The "stationary" solutions and sets possess the same properties as the
nonstationary ones and are obtainable from stationary solutions with quantum
number $p^0$ by the same boost.
  It turns out that any set can be obtained from any other by gauge
manipulations. So all sets are equivalent and the classification (i.e.
ascribing the frequency sign and in-, out- indexes) in any set is determined by
the classification in $p_3$-set, where it is evident.

2
The categories of this paper are: math
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom