The general structure and ergodic properties of quantum and classical mechanics: A unified C*-algebraic approach
| dc.creator | Duvenhage, Rocco | |
| dc.date | 2003-12-05 | |
| dc.date.accessioned | 2026-07-07T06:08:32Z | |
| dc.date.available | 2026-07-07T06:08:32Z | |
| dc.description | Quantum mechanics is essentially a statistical theory. Classical mechanics, however, is usually not viewed as being inherently statistical. Nevertheless, the latter can also be formulated statistically. Furthermore, a statistical formulation of both can be expressed in terms of unital C*-algebras, in which case it becomes clear that they have the same general structure, with quantum mechanics a noncommutative generalization of the classical case. In purely mathematical terms it is seen that quantum mechanics is a noncommutative generalization of probability theory. The most important insight in this respect is that the projection postulate of quantum mechanics is a noncommutative conditional probability. This is the subject of Chapter 1 of the thesis. As ergodic theory (the long term behaviour of a dynamical system) is done in classical probability theory, it is then also done for noncommutative probability theory in Chapter 2. In particular, generalizations of Khintchine's recurrence theorem and a variation thereof for ergodic systems are proved, as well as various characterizations of noncommutative ergodicity. Lastly, in Chapter 3, recurrence and ergodicity is then investigated from a physical perspective in quantum and classical mechanics, by means of a quantum mechanical analogue of Liouville's Theorem in classical mechanics which was suggested in Chapter 1. | |
| dc.description | PhD thesis, University of Pretoria, May 2002, 87 pages | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0312051 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0312051 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/91660 | |
| dc.subject | Quantum Physics | |
| dc.subject | Mathematical Physics | |
| dc.title | The general structure and ergodic properties of quantum and classical mechanics: A unified C*-algebraic approach | |
| dc.type | text |