Hamilton geometry: Phase space geometry from modified dispersion relations

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Barcaroli, L.; Brunkhorst, L.K.; Gubitosi, G.; Loret, N.; Pfeifer, C.: Hamilton geometry: Phase space geometry from modified dispersion relations. In: Physical Review D - Particles, Fields, Gravitation and Cosmology 92 (2015), Nr. 8, No. 84053. DOI: https://doi.org/10.1103/PhysRevD.92.084053

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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 κ-Poincaré 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. © 2015 American Physical Society.
License of this version: Es gilt deutsches Urheberrecht. Das Dokument darf zum eigenen Gebrauch kostenfrei genutzt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.
Document Type: article
Publishing status: publishedVersion
Issue Date: 2015
Appears in Collections:Fakultät für Mathematik und Physik

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1 image of flag of Germany Germany 38 90.48%
2 image of flag of United States United States 2 4.76%
3 image of flag of China China 1 2.38%
4 image of flag of Australia Australia 1 2.38%

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