Quantization of pseudoclassical systems in the Schrödinger realization

Autor:	Christopher G. Wilson, Donald Spector, Theodore J. Allen
Rok vydání:	2020
Předmět:	Physics Superselection Spinor Dynamical systems theory Phase space method Statistical and Nonlinear Physics Observable High Energy Physics::Theory symbols.namesake Quantization (physics) symbols Schrödinger picture Mathematical Physics Schrödinger's cat Mathematical physics
Zdroj:	Journal of Mathematical Physics. 61:052106
ISSN:	1089-7658 0022-2488
DOI:	10.1063/5.0003516
Popis:	We examine the quantization of pseudoclassical dynamical systems, models that have classically anticommuting variables, in the Schrodinger picture. We quantize these systems, which can be viewed as classical models of particle spin, using the generalized Gupta–Bleuler method as well as the reduced phase space method in even dimensions. With minimal modifications, the standard constructions of Schrodinger quantum mechanics of constrained systems work for pseudoclassical systems. We generalize the standard Schrodinger norm and implement the correct adjointness properties of observables and constraints. We construct the state space corresponding to spinors as physical wave functions of anticommuting variables, finding that there are superselection sectors in both the physical and ghost subspaces. The physical states are isomorphic to those of the Dirac–Kahler formulation of fermions, though the inner product in Dirac–Kahler theory is not equivalent to ours.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::47fbce47e7476d8b55613c803299622b https://doi.org/10.1063/5.0003516 Zobrazit plný text záznamu