Particle propagators on discrete spacetime

Details Particle propagators on discrete spacetime Particle propagators on discrete spacetime

2008-06-19

arxiv.org/abs/0806.3083v2

Class.Quant.Grav.25:202001,2008

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, no figures. Minor updates to match published version

Scientific paper

10.1088/0264-9381/25/20/202001

A quantum mechanical description of particle propagation on the discrete spacetime of a causal set is presented. The model involves a discrete path integral in which trajectories within the causal set are summed over to obtain a particle propagator. The sum-over-trajectories is achieved by a matrix geometric series. For causal sets generated by sprinkling points into 1+1 and 3+1 dimensional Minkowski spacetime the propagator calculated on the causal set is shown to agree, in a suitable sense, with the causal retarded propagator for the Klein-Gordon equation. The particle propagator described here is a step towards quantum field theory on causal set spacetime.

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