Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Coupled oscillators, entangled oscillators, and Lorentz-covariant
  harmonic oscillators   Other than scattering problems where perturbation theory is applicable, there
are basically two ways to solve problems in physics. One is to reduce the
problem to harmonic oscillators, and the other is to formulate the problem in
terms of two-by-two matrices. If two oscillators are coupled, the problem
combines both two-by-two matrices and harmonic oscillators. This method then
becomes a powerful research tool to cover many different branches of physics.
Indeed, the concept and methodology in one branch of physics can be translated
into another through the common mathematical formalism. Coupled oscillators
provide clear illustrative examples for some of the current issues in physics,
including entanglement and Feynman's rest of the universe. In addition, it is
noted that the present form of quantum mechanics is largely a physics of
harmonic oscillators. Special relativity is the physics of the Lorentz group
which can be represented by the group of two-by-two matrices commonly called
$SL(2,c)$. Thus the coupled harmonic oscillators can play the role of combining
quantum mechanics with special relativity. It is therefore possible to relate
the current issues of physics to the Lorentz-covariant formulation of quantum
mechanics.

1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
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
2
The categories of this paper are: math
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph