Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hamilton geometry: Phase space geometry from modified dispersion
  relations   We describe the Hamilton geometry of the phase space of particles whose
motion is characterised by general dispersion relations. In this framework
spacetime and momentum space are naturally curved and intertwined, allowing for
a simultaneous description of both spacetime curvature and non-trivial momentum
space geometry. We consider as explicit examples two models for Planck-scale
modified dispersion relations, inspired from the $q$-de Sitter and
$\kappa$-Poincar\'e quantum groups. In the first case we find the expressions
for the momentum and position dependent curvature of spacetime and momentum
space, while for the second case the manifold is flat and only the momentum
space possesses a nonzero, momentum dependent curvature. In contrast, for a
dispersion relation that is induced by a spacetime metric, as in General
Relativity, the Hamilton geometry yields a flat momentum space and the usual
curved spacetime geometry with only position dependent geometric objects.

11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int