Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The emergence of Hopf term and the marginality of Dirac model   The subtle relation of the marginality of Dirac model and the emergence of
the Hopf term through a Yukawa-type interaction is revealed in this work. We
show that the improvement of the marginality of Dirac mode through an
infinitesimal non-relativistic term, which is irrelevant for renormalization
group, is necessary to emerge the Hopf term. It is found that the appearance of
the Hopf term is always accompanied with chiral boundary modes, and the sign of
the coupling constant of the infinitesimal non-relativistic term decides their
chirality. A lattice Dirac model is also constructed to realize the Hopf term.

18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas