Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Lorentz Extension as Consequence of the Family Symmetry   In this paper we postulate an algebraic model to explain how the symmetry of
three lepton species plays its role in the Lorentz extension. Inspired by the
two-to-one mapping between the group SL (2, C) and the Lorentz group, we design
a mapping between SL (3, C) group, which displays the family symmetry, and a
generalized Lorentz group. Following the conventional method, we apply the
mapping results to Dirac equation to discuss its transformation invariance, and
it turns out that only when the vertex matrix is extended to the combination
can the Dirac-equation-form be reserved. At the same time we find that the
Lorentz group has to be extended with an additional generator . The generalized
vertex matrix is helpful in understanding the axial-like form of weak
interaction and the neutrino oscillations.

5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org