Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Relativistic dipole interaction and the topological nature for induced
  HMW and AC phases   In this work we give, for the first time, the full relativistic Lagrangian
density describing the motion of induced electric dipoles in the electric
fields which induce the dipole, and the magnetic fields which generate the HMW
topological phase. We then use this relativistic Lagrangian density to derive
the complete set of conditions for producing topological phases with induced
dipoles. We also give the relativistic Lagrangian density describing the motion
of induced magnetic dipoles in the magnetic fields which induce the dipole, and
the electric fields which generate the AC topological phase, and derive the
conditions for this AC phase to be topological. These conditions have been
incompletely discussed in previous studies. We note that, in both the AC and
HMW cases, the topological phases are generated by the cross product of
electric and magnetic fields in the form $\bm{B} \times \bm{E}$ which
reinforces the dual nature of these two topological phases.

36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int