Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Noncommutative field theory and violation of translation invariance   Noncommutative field theories with commutator of the coordinates of the form
$[x^{\mu},x^{\nu}]=i \Lambda_{\quad \omega}^{\mu \nu}x^{\omega}$ are studied.
Explicit Lorentz invariance is mantained considering $\Lambda $ a Lorentz
tensor. It is shown that a free quantum field theory is not affected. Since
invariance under translations is broken, the conservation of energy-momentum is
violated, obeying a new law which is expressed by a Poincar\'e-invariant
equation. The resulting new kinematics is studied and applied to simple
examples and to astrophysical puzzles, such as the observed violation of the
GZK cutoff.
  The $\lambda $$\Phi ^{4}$ quantum field theory is also considered in this
context. In particular, self interaction terms violate the usual conservation
of energy-momentum and, hence, the radiative correction to the propagator is
altered. The correction to first order in $\lambda $ is calculated. The usual
UV divergent terms are still present, but a new type of term also emerges,
which is IR divergent, violates momentum conservation and implies a correction
to the dispersion relation.

8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
2
The categories of this paper are: math