Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Torsion, Magnetic Monopoles and Faraday's Law via a Variational
  Principle   Even though Faraday's Law is a dynamical law that describes how changing
$\bf{E}$ and $\bf {B}$ fields influence each other, by introducing a vector
potential $A_{\mu}$ according to
$F_{\mu\nu}=\partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu}$ Faraday's Law is
satisfied kinematically, with the relation
$(-g)^{-1/2}\epsilon^{\mu\nu\sigma\tau}\nabla_{\nu}F_{\sigma\tau}=0$ holding on
every path in a variational procedure or path integral. In a space with torsion
$Q_{\alpha\beta\gamma}$ the axial vector
$S^{\mu}=(-g)^{1/2}\epsilon^{\mu\alpha\beta\gamma}Q_{\alpha\beta\gamma}$ serves
as a chiral analog of $A_{\mu}$, and via variation with respect to $S_{\mu}$
one can derive Faraday's Law dynamically as a stationarity condition. With
$S_{\mu}$ serving as an axial potential one is able to introduce magnetic
monopoles without $S_{\mu}$ needing to be singular or have a non-trivial
topology. Our analysis permits torsion and magnetic monopoles to be
intrinsically Grassmann, which could explain why they have never been detected.
Our procedure permits us to both construct a Weyl geometry in which $A_{\mu}$
is metricated and then convert it into a standard Riemannian geometry.

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The categories of this paper are: stat
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an