I investigate some algebras and calculi naturally associated with the symplectic and metric Clifford algebras. In particular, I reformulate the well known Lepage decomposition for the symplectic exterior algebra in geometrical form and present some new results relating to the simple subspaces of the decomposition. I then present an analogous decomposition for the symmetric exterior algebra with a metric. Finally, I extend this symmetric exterior algebra into a new calculus for the symmetric differential forms on a pseudo-Riemannian manifold. The importance of this calculus lies in its potential for the description of bosonic systems in Quantum Theory.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:rhodes/vital:5452 |
| Date | January 1993 |
| Creators | Russell, Neil Eric |
| Publisher | Rhodes University, Faculty of Science, Physics and Electronics |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis, Doctoral, PhD |
| Format | 185 leaves, pdf |
| Rights | Russell, Neil Eric |
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