Journal article

An Approach to Classical Quantum Field Theory Based on the Geometry of Locally Conformally Flat Space-Time

John Mashford

ADVANCES IN MATHEMATICAL PHYSICS | HINDAWI LTD | Published : 2017

Abstract

This paper gives an introduction to certain classical physical theories described in the context of locally Minkowskian causal structures (LMCSs). For simplicity of exposition we consider LMCSs which have locally Euclidean topology (i.e., are manifolds) and hence are Möbius structures. We describe natural principal bundle structures associated with Möbius structures. Fermion fields are associated with sections of vector bundles associated with the principal bundles while interaction fields (bosons) are associated with endomorphisms of the space of fermion fields. Classical quantum field theory (the Dirac equation and Maxwell's equations) is obtained by considering representations of the stru..

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Funding Acknowledgements

The work described in this paper was supported by Melbourne University, Stony Brook University, and the Commonwealth Scientific and Industrial Research Organisation (CSIRO, Australia). The author is particularly grateful to Hyam Rubinstein for supporting this work and to Iain Aitchison for very helpful discussions.