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

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RUSSELL-PhD-TR94-24.pdf 11Mb |

## 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) |
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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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