Quantum Theory Seminar
Causal Space-time on a Null Lattice
Thursday May 19, 2016 14:15:00 CEST
Thursday May 19, 2016 15:15:00 CEST
Prof. Dr. Martin Schaden, Rutgers University
Abstract: I propose a discrete model of Quantum Gravity based on the same principle as the Global Positioning System: the intersection of forward light-cones from four spatially separate events (with some restrictions) determines another event. I show that a causal manifold can thus be described by a topologically hypercubic lattice with light-like links; the length of the spatial diagonal of each plaquette being determined by spinors describing the light-like edges. This lattice model has an SL(2,C) x U^4(1) structure group and is geometric. The description foliates in a causal and physically transparent manner. The observables, the most general local action and the integration measure of this model are all determined by this stucture group and for smooth configurations have well-known continuum limits. Consistency constraints on a configuration to describe a causal manifold are derived and a one-parameter ambiguity of the invariant integration measure is exploited to regularize the model. Finally the SL(2,C) structure group is uniquely localized and the integration measure expressed in terms of geometric invariants. Should time and interest permit, I will also discuss global issues and show numerical results on a small lattice describing the vicinity of the Big Bang in the (unphysical) limit where the cosmological term dominates the dynamics.
SR 5, Helmholtzweg 4