Path integral for a relativistic Aharonov-Bohm-Coulomb system

Abstract

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

Semiclassical quantization for the spherically symmetric systems under an Aharonov-Bohm magnetic flux

“…This agrees with the exact result given in the Ref. [11]. We see that the A-B effect has changed the splitting of energy levels although the electron moves in the absence of the magnetic field.…”

“…For the system with both an A-B magnetic flux and a spherically symmetric potential of the form V (r) = λr ν (−2 < ν < ∞), the solvable models known to us include the cases with the parameter ν = −1, 0, 2, ∞ [10][11][12]16].Here λ is a constant parameter. Note that when ν = −1, it is a system with both an A-B magnetic flux and a Coulomb potential (A-B-C) [10][11][12]. This system describes the relative motion of two charged particles, with one of them carrying electric charge and magnetic flux (−q, −Φ/Z) while the other one carrying (Zq, Φ).…”

Physical Vapor Deposition of Hexagonal and Tetragonal CuIn5Se8 Thin Films

“…The starting point is the path-integral representation for the Green's function of a relativistic particle in external electromagnetic fields [4,5]:…”

Path Integral Solution of the Aharonov–Bohm–Dyon System via Summing the Perturbation Expansions

“…The starting point is the path integral representation for the Green's function of a relativistic particle in external electromagnetic fields [6][7][8],…”

“…in which ρ(λ) is an arbitrary dimensionless fluctuating scale variable, ρ(0) is the terminal point of the function ρ(λ), and [ρ(λ)] is some convenient gauge-fixing functional [6][7][8]. The only condition on [ρ(λ)] is that…”