Steven Johnston 2008 Class. Quantum Grav. 25 202001 doi:10.1088/0264-9381/25/20/202001
Particle propagators on discrete spacetime
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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.
- PACS
- MSC
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83C47 Methods of quantum field theory (See also 81T20)
83C45 Quantization of the gravitational field
83C27 Lattice gravity, Regge calculus and other discrete methods
- Subjects
- Dates
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Issue 20 (21 October 2008)
Received 23 June 2008, in final form 4 September 2008
Published 25 September 2008
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Particle propagators on discrete spacetime
Steven Johnston 2008 Class. Quantum Grav. 25 202001
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