Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Problem of constructing discrete and finite quantum theory   We consider in detail an approach (proposed by the author earlier) where
quantum states are described by elements of a linear space over a Galois field,
and operators of physical quantities - by linear operators in this space. The
notion of Galois fields (which is extremely simple and elegant) is discussed in
detail and we also discuss the conditions when our description gives the same
predictions as the conventional one. In quantum theory based on a Galois field,
all operators are well defined and divergencies cannot not exist in principle.
A particle and its antiparticle are described by the same modular irreducible
representation of the symmetry algebra. This automatically explains the
existence of antiparticles and shows that a particle and its antiparticle are
the different states of the same object. As a consequence, a new symmetry
arises, and the structure of the theory is considerably simplified. In
particular, one can work with only creation operators or only annihilation ones
since they are no more independent. In our approach the problem arises whether
the existence of neutral elementary particles (e.g. the photon) is compatible
with the usual relation between spin and statistics, or in other words whether
neutral particles can be elementary or only composite.

24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
2
The categories of this paper are: math
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas