An Approach to Classical Quantum Field Theory Based on the Geometry of Locally Conformally Flat Space-Time
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 n...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2017-01-01
|
| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2017/8070462 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832567876728389632 |
|---|---|
| author | John Mashford |
| author_facet | John Mashford |
| author_sort | John Mashford |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-7fab2d7980454c7e87f19762e834e375 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-7fab2d7980454c7e87f19762e834e3752025-02-03T01:00:17ZengWileyAdvances in Mathematical Physics1687-91201687-91392017-01-01201710.1155/2017/80704628070462An Approach to Classical Quantum Field Theory Based on the Geometry of Locally Conformally Flat Space-TimeJohn Mashford0School of Mathematics and Statistics, University of Melbourne, Parkville, VIC 3010, AustraliaThis 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.http://dx.doi.org/10.1155/2017/8070462 |
| spellingShingle | John Mashford An Approach to Classical Quantum Field Theory Based on the Geometry of Locally Conformally Flat Space-Time Advances in Mathematical Physics |
| title | An Approach to Classical Quantum Field Theory Based on the Geometry of Locally Conformally Flat Space-Time |
| title_full | An Approach to Classical Quantum Field Theory Based on the Geometry of Locally Conformally Flat Space-Time |
| title_fullStr | An Approach to Classical Quantum Field Theory Based on the Geometry of Locally Conformally Flat Space-Time |
| title_full_unstemmed | An Approach to Classical Quantum Field Theory Based on the Geometry of Locally Conformally Flat Space-Time |
| title_short | An Approach to Classical Quantum Field Theory Based on the Geometry of Locally Conformally Flat Space-Time |
| title_sort | approach to classical quantum field theory based on the geometry of locally conformally flat space time |
| url | http://dx.doi.org/10.1155/2017/8070462 |
| work_keys_str_mv | AT johnmashford anapproachtoclassicalquantumfieldtheorybasedonthegeometryoflocallyconformallyflatspacetime AT johnmashford approachtoclassicalquantumfieldtheorybasedonthegeometryoflocallyconformallyflatspacetime |