Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetry of Dirac Equation and Corresponding Phenomenology   It has been suggested that the high symmetries in the Schr\"odinger equation
with the Coulomb or harmonic oscillator potentials may remain in the
corresponding relativistic Dirac equation. If the principle is correct, in the
Dirac equation the potential should have a form as ${(1+\beta)\over 2}V(r)$
where $V(r)$ is ${-e^2\over r}$ for hydrogen atom and $\kappa r^2$ for harmonic
oscillator. However, in the case of hydrogen atom, by this combination the
spin-orbit coupling term would not exist and it is inconsistent with the
observational spectra of hydrogen atom, so that the symmetry of SO(4) must
reduce into SU(2). The governing mechanisms QED and QCD which induce potential
are vector-like theories, so at the leading order only vector potential exists.
However, the higher order effects may cause a scalar fraction. In this work, we
show that for QED, the symmetry restoration is very small and some discussions
on the symmetry breaking are made. At the end, we briefly discuss the QCD case
and indicate that the situation for QCD is much more complicated and
interesting.

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The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
3
The categories of this paper are: physics
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th