Path integral treatment of two- and three-dimensional delta-function potentials and application to spin-1/2 Aharonov-Bohm problem

Abstract

Delta-function potentials in two- and three-dimensional quantum mechanics are analyzed by the incorporation of the self-adjoint extension method to the path integral formalism. The energy-dependent Green functions for free particle plus delta-function potential systems are explicitly calculated. Also the energy-dependent Green function for the spin-1/2 Aharonov-Bohm problem is evaluated. It is found that the only one special value of the self-adjoint extension parameter gives a well-defined and non-trivial time-dependent propagator. This special value corresponds to the viewpoint of the spin-1/2 Aharonov-Bohm problem when the delta-function is treated as a limit of the infinitesimal radius.

21 pages Latex

References in corpus (4)

• Path Integration Via Summation of Perturbation Expansions and Applications to Totally Reflecting Boundaries, and Potential Steps
• Self-adjoint Extension Approach to the spin-1/2 Aharonov-Bohm-Coulomb Problem
• ${\delta }^{\prime }$-Function Perturbations and Neumann Boundary-Conditions by Path Integration
• Path Integral Discussion of Two and- Three-Dimensional $\delta$-Function Perturbations

Cited by in corpus (32)

• Energy Spectrum of a 2D Dirac Oscillator in the Presence of the Aharonov-Bohm Effect
• Physical regularization for the spin-1/2 Aharonov-Bohm problem in conical space
• Effects of spin on the dynamics of the 2D Dirac oscillator in the magnetic cosmic string background
• On the spin-1/2 Aharonov-Bohm problem in conical space: bound states, scattering and helicity nonconservation
• Green functions for generalized point interactions in 1D: A scattering approach
• Exact solution for a quantum field with $\delta$-like interaction
• Renormalized Path Integral for the Two-Dimensional Delta-Function Interaction
• One-Dimensional Semirelativistic Hamiltonian with Multiple Dirac Delta Potentials
• On Aharonov-Casher bound states
• Point Interaction in two and three dimensional Riemannian Manifolds
• Proper incorporation of self-adjoint extension method to Green's function formalism : one-dimensional ${\delta }^{{}^{\prime }}$-function potential case
• Finitely Many Dirac-Delta Interactions on Riemannian Manifolds
• Single 3-Brane Brane-World in Six Dimension
• GUP and Point Interaction
• Green functions of the Dirac equation with magnetic-solenoid field
• Path Integral Discussion of Two and- Three-Dimensional $\delta$-Function Perturbations
• Propagator for spinless and spin-1/2 Aharonov-Bohm-Coulomb systems
• Generalized uncertainty principle and $D$-dimensional quantum mechanics
• Newton Law on the Generalized Singular Brane with and without 4d Induced Gravity
• Local realizations of contact interactions in two- and three-body problems
• Singular perturbations with boundary conditions and the Casimir effect in the half space
• Interaction of Relativistic Bosons with Localized Sources on Riemannian Surfaces
• Directed Polymers with Constrained Winding Angle
• Compromise of Localized Graviton with a Small Cosmological Constant in Randall-Sundrum Scenario
• Scattering and bound states of a spin--1/2 neutral particle in the cosmic string spacetime
• Self-adjoint extension approach for singular Hamiltonians in (2+1) dimensions
• Newton Law in Brane-World Scenario with 4d Induced Gravity: Singular Quantum Mechanical Approach
• Singular Quantum Mechanical Viewpoint of Localized Gravity in Brane-World Scenario
• Renormalization in Wavelet basis
• Aharonov-Bohm-Coulomb Problem in Graphene Ring
• Finite temperature quantum field theory on non compact domains and application to delta interactionsinteractions in three dimensions
• Aharonov-Bohm-Like Scattering in the Generalized Uncertainty Principle-corrected Quantum Mechanics