## Potential canonical framework for quantum-classical dynamics

2021
##### Authors
Amin Hemeida, Mustafa
University of Lethbridge. Faculty of Arts and Science
##### Publisher
Lethbridge, Alta. : University of Lethbridge, Dept. of Physics and Astronomy
##### Abstract
Dynamical brackets lie at the heart of fundamental physical theories. They are Lie brackets that obey the Leibniz rule with respect to a suitable composition product. The pair composition product'' and dynamical bracket'' define a formal dynamical structure that is common to classical and quantum mechanics. Without properties like the Jacobi identity and the Leibniz rule, the consistency of a dynamical framework cannot be guaranteed. This work investigates the possibility of combining quantum and classical dynamics into a single, consistent framework. We generalize previous attempts and discuss no-go theorems that assert their inconsistency. We show that the Jacobi identity and Leibniz rule are satisfied provided there exists an associative product for hybrid variables. This condition motivates the construction of associative subalgebras over which quantum-classical dynamics is consistent: perhaps hybrid observables are constrained to belong to such algebras. If so, only certain interactions between quantum and classical systems would be allowed.
##### Keywords
physics , classical mechanics , quantum mechanics , hybrid mechanics , quantum-classical interaction , quantum-classical mechanics , Mechanics , Quantum theory , Phase space (Statistical physics) , Dissertations, Academic