Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Lorentz Group, Noncommutative Space-Time, and Nonlinear
  Electrodynamics in Majorana-Oppenheimer Formalism   Non-linear electrodynamics arising in the frames of field theories in
non-commutative space-time is examined on the base of the
Riemann-Silberstein-Majorana-Oppenheimer formalism. The problem of
form-invariance of the non-linear constitutive relations governed by six
non-commutative parameters \theta_{kl} \sim {\bf K} = {\bf n} + i {\bf m} is
explored in detail on the base of the complex orthogonal group theory SO(3.C).
Two Abelian 2-parametric small groups, isomorphic to each other in abstract
sense, and leaving unchangeable the extended constitutive relations at
arbitrary six parameters \theta_{kl} of effective media have been found, their
realization depends explicitly on invariant length {\bf K}^{2}. In the case of
non-vanishing length a special reference frame in which the small group has the
structure SO(2) \otimes SO(1,1) has been found. In isotropic case no such
reference frame exists. The way to interpret both Abelian small groups in
physical terms consists in factorizing corresponding Lorentz transformations
into Euclidean rotations and boosts. In the context of general study of various
dual symmetries in non-commutative field theory, it is demonstrated explicitly
that the non-linear constitutive equations in non-commutative electrodynamics
are not invariant under continuous dual rotations, instead only invariance
under discrete dual transformation exists.

18
The categories of this paper are: econ
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
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