Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the derivation of an effective Higgs field   In one respect, the massive vector-boson shows its difference from a massless
vector-boson by one more physical polarization, known as longitudinal
polarization. In another respect, the quantized boson acquires its mass by
Higgs mechanism. In this paper we study the effect of the longitudinal
polarization in U(1) case by substituting it into the primary Yang-Mills
Lagrangian $-\frac 14F_{\mu \nu}F^{\mu \nu}$. Under a hypothesis of strong
transversal condition for free vector boson, it is found that in the Lagrangian
the scalar field for the Higgs mechanism can automatically arise after we
separate a part equivalent to the contribution of a massless boson. In
addition, a criterion is obtained to infer whether the boson is massive or not:
if $\mathbf{E}^2-\mathbf{B}^2\neq 0$, where $\mathbf{E}$ and $\mathbf{B}$ are
field strengths, then it is massive. The analysis also pertains to SU(2) case.
The method in this paper is performed before any quantizations.

18
The categories of this paper are: econ
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg