Russell, Neil Eric (1993) Aspects of the symplectic and metric geometry of classical and quantum physics. PhD thesis, Rhodes University.
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|
|Deposited By:||Mrs Carol Perold|
|Deposited On:||01 Nov 2012 08:27|
|Last Modified:||01 Nov 2012 08:27|
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