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

Russell, Neil Eric (1993) Aspects of the symplectic and metric geometry of classical and quantum physics. PhD thesis, Rhodes University.

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Abstract

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.

Item Type:Thesis (PhD)
Uncontrolled Keywords:Symplectic manifolds, Differential geometry, Quantum theory, Clifford algebras, Geometric quantization
Subjects:Q Science > QC Physics
Divisions:Faculty > Faculty of Science > Physics & Electronics
ID Code:3925
Deposited By: Mrs Carol Perold
Deposited On:01 Nov 2012 08:27
Last Modified:01 Nov 2012 08:27
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