2010/10/26 by Steven Johnston, Johnston, Steven
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #gr-qc #hep-th
paper · pdf · doi:10.48550/arxiv.1010.5514
PhD Thesis, Imperial College London, September 2010
arxiv created 2010/10/26 · openalex publication_date 2010/10/26 · arxiv updated 2010/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Causal set theory provides a model of discrete spacetime in which spacetime events are represented by elements of a causal set---a locally finite, partially ordered set in which the partial order represents the causal relationships between events. The work presented here describes a model for matter on a causal set, specifically a theory of quantum scalar fields on a causal set spacetime background. The work starts with a discrete path integral model for particles on a causal set. Here quantum mechanical amplitudes are assigned to trajectories within the causal set. By summing these over all trajectories between two spacetime events we obtain a causal set particle propagator. With a suitable choice of amplitudes this is shown to agree (in an appropriate sense) with the retarded propagator for the Klein-Gordon equation in Minkowski spacetime. This causal set propagator is then used to define a causal set analogue of the Pauli-Jordan function that appears in continuum quantum field theories. A quantum scalar field is then modelled by an algebra of operators which satisfy three simple conditions (including a bosonic commutation rule). Defining time-ordering through a linear extension of the causal set these field operators are used to define a causal set Feynman propagator. Evidence is presented which shows agreement (in a suitable sense) between the causal set Feynman propagator and the continuum Feynman propagator for the Klein-Gordon equation in Minkowski spacetime. The Feynman propagator is obtained using the eigendecomposition of the Pauli-Jordan function, a method which can also be applied in continuum-based theories. The free field theory is extended to include interacting scalar fields. This leads to a suggestion for a non-perturbative S-matrix on a causal set. Models for continuum-based phenomenology and spin-half particles on a causal set are also presented.