An Approach to Classical Quantum Field Theory Based on the Geometry of Locally Conformally Flat Space-Time
Author
Source
Advances in Mathematical Physics
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-10-19
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
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 structure group K⊂SU(2,2) of a principal bundle associated with a given Möbius structure where K, while being a subset of SU(2,2), is also isomorphic to SL2,C×U(1).
The analysis requires the use of an intertwining operator between the action of K on R4 and the adjoint action of K on su(2,2) and it is shown that the Feynman slash operator, in the chiral representation for the Dirac gamma matrices, has this intertwining property.
American Psychological Association (APA)
Mashford, John. 2017. An Approach to Classical Quantum Field Theory Based on the Geometry of Locally Conformally Flat Space-Time. Advances in Mathematical Physics،Vol. 2017, no. 2017, pp.1-15.
https://search.emarefa.net/detail/BIM-1123310
Modern Language Association (MLA)
Mashford, John. An Approach to Classical Quantum Field Theory Based on the Geometry of Locally Conformally Flat Space-Time. Advances in Mathematical Physics No. 2017 (2017), pp.1-15.
https://search.emarefa.net/detail/BIM-1123310
American Medical Association (AMA)
Mashford, John. An Approach to Classical Quantum Field Theory Based on the Geometry of Locally Conformally Flat Space-Time. Advances in Mathematical Physics. 2017. Vol. 2017, no. 2017, pp.1-15.
https://search.emarefa.net/detail/BIM-1123310
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1123310