Path integral in position-deformed Heisenberg algebra with maximal length uncertainty
Date
2023
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Annals of Physics
Abstract
In this work, we study the path integral in a position-deformed
Heisenberg algebra with quadratic deformation which imple ments both minimal momentum and maximal length uncer tainties. We construct propagators of path integrals within this
deformed algebra using the position space representation on the
one hand and the Fourier transform and its inverse representa tions on the other. The result is remarkably similar to the one
obtained by Pramanik (2022) from the Perivolaropoulos’s de formed algebra (Perivolaropoulos, 2017). Then, the propagators
and the corresponding actions of a free particle and a simple
harmonic oscillator are discussed as examples. We also show
that the actions which describe the classical trajectories of both
systems are bounded by the ordinary ones of classical mechanics
due to the existence of this maximal length. Consequently, par ticles of these systems travel faster from one point to another
with low kinetic and mechanical energies.
Description
Research Article
Keywords
Generalized uncertainty principle, Quantum gravity, Path integral, Propagator and action