- Title
- Aspects of the symplectic and metric geometry of classical and quantum physics
- Creator
- Russell, Neil Eric
- Subject
- Symplectic manifolds Geometry, Differential Geometric quantization Quantum theory Clifford algebras
- Date Issued
- 1993
- Date
- 1993
- Type
- Thesis
- Type
- Doctoral
- Type
- PhD
- Identifier
- vital:5452
- Identifier
- http://hdl.handle.net/10962/d1005237
- Description
- 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.
- Format
- 185 leaves
- Format
- Publisher
- Rhodes University
- Publisher
- Faculty of Science, Physics and Electronics
- Language
- English
- Rights
- Russell, Neil Eric
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