期刊
PHYSICAL REVIEW D
卷 92, 期 8, 页码 -出版社
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevD.92.084053
关键词
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资金
- Center of Applied Space Technology and Microgravity (ZARM) at the University of Bremen
- John Templeton Foundation [47633, 29085]
- German Research Foundation
We describe the Hamilton geometry of the phase space of particles whose motion is characterized 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 nontrivial momentum space geometry. We consider as explicit examples two models for Planck-scale modified dispersion relations, inspired from the q-de Sitter and kappa-Poincare 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.
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