MG14 - Talk detail

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Abstract

Quantum gravity phenomenology suggests an effective modification of the general relativistic dispersion relation of freely falling point particles caused by an underlying theory of quantum gravity. In this talk I will analyse the consequences of modifications of the general relativistic dispersion on the geometry of spacetime in the language of Hamilton geometry. The dispersion relation is interpreted as the Hamiltonian which determines the motion of point particles. It is a function on the cotangent bundle of spacetime, i.e. on phase space, and determines the geometry of phase space completely, similarly as the metric determines the geometry of spacetime in general relativity. After a review of the general Hamilton geometry of phase space I will discuss two examples. The phase space geometry of the metric Hamiltonian Hg(x,p)=g(p,p) and the phase space geometry of the first order q-DeSitter dispersion relation of the form HqDS(x,p)=g(p,p) + L h(p,p,p) which is suggested from quantum gravity phenomenology. We will see that for the metric Hamiltonian Hg the geometry of phase space is equivalent to the standard metric spacetime geometry from general relativity. For the q-DeSitter Hamiltonian HqDS the Hamilton equations of motion for point particles do not become autoparallels but contain a force term, the momentum space part of phase space is curved and the curvature of spacetime becomes momentum dependent.

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