Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lattice implementation of Abelian gauge theories with Chern-Simons
  number and an axion field   Real time evolution of classical gauge fields is relevant for a number of
applications in particle physics and cosmology, ranging from the early Universe
to dynamics of quark-gluon plasma. We present a lattice formulation of the
interaction between a $shift$-symmetric field and some $U(1)$ gauge sector,
$a(x)\tilde{F}_{\mu\nu}F^{\mu\nu}$, reproducing the continuum limit to order
$\mathcal{O}(dx_\mu^2)$ and obeying the following properties: (i) the system is
gauge invariant and (ii) shift symmetry is exact on the lattice. For this end
we construct a definition of the {\it topological number density} $Q =
\tilde{F}_{\mu\nu}F^{\mu\nu}$ that admits a lattice total derivative
representation $Q = \Delta_\mu^+ K^\mu$, reproducing to order
$\mathcal{O}(dx_\mu^2)$ the continuum expression $Q = \partial_\mu K^\mu
\propto \vec E \cdot \vec B$. If we consider a homogeneous field $a(x) = a(t)$,
the system can be mapped into an Abelian gauge theory with Hamiltonian
containing a Chern-Simons term for the gauge fields. This allow us to study in
an accompanying paper the real time dynamics of fermion number non-conservation
(or chirality breaking) in Abelian gauge theories at finite temperature. When
$a(x) = a(\vec x,t)$ is inhomogeneous, the set of lattice equations of motion
do not admit however a simple explicit local solution (while preserving an
$\mathcal{O}(dx_\mu^2)$ accuracy). We discuss an iterative scheme allowing to
overcome this difficulty.

30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex