Path integral for a relativistic spinless Coulomb system

Abstract

The path integral of the relativistic Coulomb system is solved, and the wave functions are extracted from the resulting amplitude.

Path integral for a relativistic Aharonov-Bohm-Coulomb system

“…Adding a vector potential A(x) to Kleinert's relativistic path integral for a particle in a potential V (x) [4,2], we find the expression for the fixed-energy amplitude…”

“…Only recently has the technique been extended to relativistic potential problems [4], followed by two applications [5][6][7][8]. Here we'd like to add a further application by solving the path integral of relativistic particle in two dimensions in the presence of an infinitely thin Aharonov-Bohm magnetic field along the z-axis [9] and a 1/r-Coulomb potential (ABC system).…”

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

“…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…”

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

Green's function for the relativistic Coulomb system via sum over perturbation series

“…where S is defined by , to fix the value of ρ(λ) to unity [11,12].h/Mc is the well-known Compton wave length of a particle of mass M, A(x) is the vector potential, V (x) is the scalar potential, E is the system energy, and x is the spatial part of the (D + 1) vector x = (x, τ ). This path integral forms the basis for studying relativistic potential problems.…”