The ill-posed problem of quantizing space-time is replaced by a more determined and well-posed problem of regularizing quantum dynamics.
The problem is then to eliminate the Heisenberg singularity from quantum mechanics as economically as possible.
The concepts of regular and singular groups are explained and the Heisenberg singularity defined. This singularity infests not only the theory of space-time,
but also the Bose-Einstein statistics and the theory of the gauge fields and interactions. It is responsible for most of the infinities of present quantum field theory.
The key new conceptual step is to turn attention from observables to "dynamicals", the observable-valued-functions of time which actually enters into the Heisenberg dynamical equations. The dynamicals have separate algebras from the algebra and Lie algebra of the observables. This reconception allows for the possibility of clock-system entanglement that is missing from the usual singular dynamics, and implied by the concept of quantum space-time.
The dynamical Lie algebra and the resulting Lie group are regularized for an example system, the time-dependent isotropic harmonic oscillator of arbitrary finite dimension. The result is a quantize space-time, but also momentum-energy and every other dynamical variable in the theory. This method is readily extended to general dynamic quantum systems.
| Identifer | oai:union.ndltd.org:GATECH/oai:smartech.gatech.edu:1853/4866 |
| Date | 01 December 2004 |
| Creators | Baugh, James Emory |
| Publisher | Georgia Institute of Technology |
| Source Sets | Georgia Tech Electronic Thesis and Dissertation Archive |
| Language | en_US |
| Detected Language | English |
| Type | Dissertation |
| Format | 279129 bytes, application/pdf |
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