Understand
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.
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