Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics A Mathematical and General

Exact Green's function of the Aharonov-Bohm-Coulomb system via the Feynman-Kac formula

Der-San Chuu, De‐Hone Lin

Published Sep 15, 1999• 3 citations
Publisher

Abstract

The Green's function of the relativistic Aharonov-Bohm-Coulomb system is given by the Feynman-Kac formula. The earlier treatment is based on the multiple-valued transformation of Levi-Civitá . The method used in this contribution involves only the explicit form of a simple Green's function and an explicit path integral is avoided.

DOI
10.1088/0305-4470/32/39/306

Related papers

Path integral solution by sum over perturbation series

De‐Hone Lin

A method for calculating the relativistic path integral solution via sum over perturbation series is given. As an application the exact path integral solution of the relativistic Aharonov–Bohm–Coulomb system is obtained by the method. Different from the earlier treatment based on the space–time transformation and infinite multiple-valued trasformation of Kustaanheimo–Stiefel in order to perform path integral, the method developed in this contribution involves only the explicit form of a simple Green’s function and an explicit path integral is avoided.

arXiv:quant-ph/9909050•Journal of Mathematical Physics•May 1, 2000•9 citations

Quantum Aharonov-Bohm Billiard System

Der-San Chuu, De‐Hone Lin

The Green's functions of the two and three-dimensional relativistic Aharonov-Bohm (A-B) systems are given by the path integral approach. In addition the exact radial Green's functions of the spherical A-B quantum billiard system in two and three-dimensional are obtained via the perturbation techanique of $δ$-function.

arXiv:chao-dyn/9909022•Sep 15, 1999•0 citations

Exact path integral solution of the Coulomb plus Aharonov–Bohm potential

L. Chétouani, Larbi Guechi, Théophile F. Hammann

The Green’s function for the sum of the Coulomb and Aharonov–Bohm potentials is calculated exactly in the path integral formalism. The energy spectrum is deduced.

Journal of Mathematical Physics•Mar 1, 1989•37 citations

Dirac particle in Aharonov–Bohm–Coulomb field: Path integral treatment

Abdeldjalil Merdaci, N. Boudiaf, L. Chétouani

Exact Green’s function related to a Dirac particle submitted to the combination of Aharonov–Bohm and Coulomb potentials in [Formula: see text]) coordinate space is analytically calculated via path integral formalism. The Pauli matrices which describe the spin dynamics are replaced by two fermionic oscillators via the Schwinger model. The energy spectrum as well as the corresponding normalized wave functions are extracted following this approach. The interesting properties of the spinors are thus deduced after symmetrization. According to the symmetric form for Green’s function, it is shown that the non-relativistic limit of the Dirac particle is undertaken with much ease.

Modern Physics Letters A•Dec 21, 2021•0 citations

Path integral for a relativistic Aharonov-Bohm-Coulomb system

De‐Hone Lin

The path integral for the relativistic spinless Aharonov-Bohm-Coulomb system is performed. The energy spectra and wavefunctions are extracted from the resulting amplitude.

arXiv:hep-th/9708125•Journal of Physics A Mathematical and General•May 22, 1998•20 citations

Green’s Function for the Aharonov-Bohm Effect with a Non-Abelian Gauge Group

Pavel Šťovíček

In the case of more than one solenoid, the computation of the Green’s function for the Aharonov-Bohm effect becomes rather complicated. In this paper, we discuss two possible approaches to this problem. We start with the Schulman’s approach based on the Feynman path integral. Applying this technique, recently having been generalized by several authors to non-Abelian gauge groups, we are able to derive some explicit formulae in the two-solenoid case. On the other hand, the interpretation of the problem in the framework of the theory of self-adjoint extensions allows us to apply the Krein’s formula. But in this case, some open problems still remain.

Birkhäuser Basel eBooks•Jan 1, 1990•0 citations
The Green's function of the relativistic Aharonov-Bohm-Coulomb system is given by the Feynman-Kac formula. The earlier treatment is based on the multiple-valued transformation of Levi-Civitá . The method used in this contribution involves only the explicit form of a simple Green's function and an explicit path integral is avoided.
A method for calculating the relativistic path integral solution via sum over perturbation series is given. As an application the exact path integral solution of the relativistic Aharonov–Bohm–Coulomb system is obtained by the method. Different from the earlier treatment based on the space–time transformation and infinite multiple-valued trasformation of Kustaanheimo–Stiefel in order to perform path integral, the method developed in this contribution involves only the explicit form of a simple Green’s function and an explicit path integral is avoided.
The Green's functions of the two and three-dimensional relativistic Aharonov-Bohm (A-B) systems are given by the path integral approach. In addition the exact radial Green's functions of the spherical A-B quantum billiard system in two and three-dimensional are obtained via the perturbation techanique of δδδ-function.
Exact Green’s function related to a Dirac particle submitted to the combination of Aharonov–Bohm and Coulomb potentials in [Formula: see text]) coordinate space is analytically calculated via path integral formalism. The Pauli matrices which describe the spin dynamics are replaced by two fermionic oscillators via the Schwinger model. The energy spectrum as well as the corresponding normalized wave functions are extracted following this approach. The interesting properties of the spinors are thus deduced after symmetrization. According to the symmetric form for Green’s function, it is shown that the non-relativistic limit of the Dirac particle is undertaken with much ease.
In the case of more than one solenoid, the computation of the Green’s function for the Aharonov-Bohm effect becomes rather complicated. In this paper, we discuss two possible approaches to this problem. We start with the Schulman’s approach based on the Feynman path integral. Applying this technique, recently having been generalized by several authors to non-Abelian gauge groups, we are able to derive some explicit formulae in the two-solenoid case. On the other hand, the interpretation of the problem in the framework of the theory of self-adjoint extensions allows us to apply the Krein’s formula. But in this case, some open problems still remain.