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arXiv · 0806.3083

Particle propagators on discrete spacetime

Steven Johnston
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Abstract

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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Steven Johnston. 2008-10-01. Particle propagators on discrete spacetime. https://doi.org/10.1088/0264-9381%2F25%2F20%2F202001

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