Dirac’s Formalism for Time-Dependent Hamiltonian Systems in the Extended Phase Space

Garcia-Chung, Angel; García-Ruíz, Daniel; Vergara, David

doi:10.3390/universe7040109

Dirac’s Formalism for Time-Dependent Hamiltonian Systems in the Extended Phase Space

Journal

Universe

ISSN

2218-1997

Date Issued

2021

Author(s)

Garcia-Chung, Angel

Facultad de Ingeniería - CampCM

García-Ruíz, Daniel

Vergara, David

Type

text::journal::journal article

DOI

10.3390/universe7040109

URL

https://scripta.up.edu.mx/handle/20.500.12552/4384

Abstract

Dirac’s formalism for constrained systems is applied to the analysis of time-dependent Hamiltonians in the extended phase space. We show that the Lewis invariant is a reparametrization invariant, and we calculate the Feynman propagator using the extended phase space description. We show that the Feynman propagator’s quantum phase is given by the boundary term of the canonical transformation of the extended phase space. We propose a new canonical transformation within the extended phase space that leads to a Lewis invariant generalization, and we sketch some possible applications. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.