Aspects of the symplectic and metric geometry of classical and quantum physics

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: 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, pdf
Publisher: Rhodes University, Faculty of Science, Physics and Electronics
Language: English
Rights: Russell, Neil Eric

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