Path integration on the hyperbolic plane with a magnetic field
type: Item
instance of: scholarly article
title: Path integration on the hyperbolic plane with a magnetic field
zbMATH Open document ID: 0724.58017
DOI: 10.1016/0003-4916(90)90042-M
author: Christian Grosche
published in: Annals of Physics
publication date: 1990-01-01T00:00:00Z
review text: The author discusses the path integrals on three formulations of hyperbolic geometry, where a constant magnetic field B is included. These are: the pseudo-sphere, the Poincaré disc, and the hyperbolic strip. The corresponding path integrals can be reformulated in terms of the path integral for the modified Pöschl-Teller potential. The wave-functions and the energy spectrum for the discrete and continuous part of the spectrum are explicitly calculated in each case. First the results are compared for the limit \(B\to 0\) with previous calculations and second with the path integration on the Poincaré upper half-plane.
Mathematics Subject Classification ID: 58D30
Mathematics Subject Classification ID: 81Q30
zbMATH DE Number: 4194750
zbMATH Keywords: Feynman integrals
zbMATH Keywords: path integrals
zbMATH Keywords: hyperbolic geometry
zbMATH Keywords: constant magnetic field
reviewed by: Klaus Brod
MaRDI profile type: Publication
Wikidata QID: Q125800604
cites work: Path integrals in polar coordinates
cites work: Path integral treatment of the hydrogen atom in a curved space of constant curvature
cites work: Path integration over compact and noncompact rotation groups
cites work: Dynamical Theory in Curved Spaces. I. A Review of the Classical and Quantum Action Principles
cites work: Fourier coefficients of the resolvent for a Fuchsian group.
cites work: Space-Time Approach to Non-Relativistic Quantum Mechanics
cites work: Path−integral evaluation of a nonstationary Calogero model
cites work: Q3671491
cites work: Q3756080
cites work: The path integral on the Poincaré upper half-plane with a magnetic field and for the Morse potential
cites work: The path integral on the pseudosphere
cites work: Handbook of Feynman path integrals
cites work: The Geometry of Quantum Chaos
cites work: The Selberg trace formula for \(\mathrm{PSL}(2,\mathbb R)\). Vol. I
cites work: Q5518575
cites work: Q4083962
cites work: Q4754267
cites work: Q5845868
cites work: Q3714308
cites work: Q3237356
cites work: Q5559954
full work available at URL: 0003-4916(90)90042-m
OpenAlex ID: W2110886485
description: scientific article; zbMATH DE number 4194750