The relation between the symplectic group Sp(4,R) and its Lie algebra: Applications to polymer quantum mechanics

Chacón-Acosta, Guillermo; Garcia-Chung, Angel

doi:10.1103/PhysRevD.104.126006

The relation between the symplectic group Sp(4,R) and its Lie algebra: Applications to polymer quantum mechanics

Journal

Physical Review D

ISSN

2470-0010

2470-0029

Date Issued

2021

Author(s)

Chacón-Acosta, Guillermo

Garcia-Chung, Angel

Facultad de Ingeniería - CampCM

Type

text::journal::journal article

DOI

10.1103/PhysRevD.104.126006

URL

https://scripta.up.edu.mx/handle/20.500.12552/4326

Abstract

In this paper, we show the relation between sp(4,R), the Lie algebra of the symplectic group, and the elements of Sp(4,R). We use this result to obtain some special cases of symplectic matrices relevant to the study of squeezed states. In this regard, we provide some applications in quantum mechanics and analyze the squeezed polymer states obtained from the polymer representation of the symplectic group. Remarkably, the polymer's dispersions are the same as those obtained for the squeezed states in the usual representation. © 2021 American Physical Society.