Augmenting phase space quantization to introduce additional physical effects

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Robbins, Matthew P. G.
University of Lethbridge. Faculty of Arts and Science
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Lethbridge, Alta : University of Lethbridge, Dept. of Physics and Astronomy
Quantum mechanics can be done using classical phase space functions and a star product. The state of the system is described by a quasi-probability distribution. A classical system can be quantized in phase space in different ways with different quasi-probability distributions and star products. A transition differential operator relates different phase space quantizations. The objective of this thesis is to introduce additional physical effects into the process of quantization by using the transition operator. As prototypical examples, we first look at the coarse-graining of the Wigner function and the damped simple harmonic oscillator. By generalizing the transition operator and star product to also be functions of the position and momentum, we show that additional physical features beyond damping and coarse-graining can be introduced into a quantum system, including the generalized uncertainty principle of quantum gravity phenomenology, driving forces, and decoherence.
augmented quantization , phase space quantum mechanics , quantization , star product , transition operator