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

Universe

Angel Garcia-Chung¹  J.David Vergara²  Daniel Gutiérrez-Ruiz² 

[1] Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, San Rafael Atlixco 186, Ciudad de México C.P. 09340, Mexico;Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Ciudad Universitaria, Ciudad de México C.P. 04510, Mexico;

关键词: time-dependent quantum mechanics;    quantum cosmology;    path integrals;   

DOI  :  10.3390/universe7040109

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown