Hamburg 2016 – wissenschaftliches Programm
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GR: Fachverband Gravitation und Relativitätstheorie
GR 13: Quantum Gravity III
GR 13.4: Vortrag
Donnerstag, 3. März 2016, 17:45–18:05, VMP6 HS A
Hamilton geometry - Dispersion relations and the geometry of spacetime — •Christian Pfeifer — ITP Uni Hannover, Hannover, Deutschland
One feature how a fundamental theory of quantum gravity is expected to manifest itself in observations is an effective modification of the standard dispersion relation of fundamental point particles in metric spacetime geometry. Since the point particle dispersion relation and the geometry of spacetime are closely intertwined any modification of the dispersion relation leads to a, possibly energy and momentum dependent, modification of the geometry of spacetime. In this talk I will interpret the dispersion relation as Hamilton function on the phase space of test particles on spacetime and show how one can derive the geometry of phase space from the Hamiltonian, similarly as one derives the geometry of spacetime from a metric. Since phase space is composed out of spacetime (configuration space) and momentum space the result for a general Hamiltonian is that not only the spacetime is curved but also the momentum space. Moreover, both, the curvature of spacetime and that of momentum space, depend in general on positions and momenta. I will demonstrate this framework on the example of a perturbation of the metric Hamiltonian H=g−1(p,p)+ ℓ h(p,p,p) which contains as special cases famous models used in quantum gravity phenomenology.