Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Discrete Time Evolution and Energy Nonconservation in Noncommutative
  Physics   Time-space noncommutativity leads to quantisation of time and energy
nonconservation when time is conjugate to a compact spatial direction like a
circle. In this context energy is conserved only modulo some fixed unit. Such a
possibility arises for example in theories with a compact extra dimension with
which time does not commute. The above results suggest striking
phenomenological consequences in extra dimensional theories and elsewhere. In
this paper we develop scattering theory for discrete time translations. It
enables the calculation of transition probabilities for energy nonconserving
processes and has a central role both in formal theory and phenomenology.
  We can also consider space-space noncommutativity where one of the spatial
directions is a circle. That leads to the quantisation of the remaining spatial
direction and conservation of momentum in that direction only modulo some fixed
unit, as a simple adaptation of the results in this paper shows.

29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ