The Froissart-Gribov representation of Jost function of Dirac operators in arbitrary-dimension space

TL;DR

This paper introduces a new dynamic scheme and generalizes the off-shell-Jost function method for Dirac and Schrödinger operators in arbitrary dimensions, handling singular and nonlocal potentials.

Contribution

It proposes a novel dynamic scheme and universal renormalization procedure for calculating Jost functions of local Dirac and Schrödinger Hamiltonians in arbitrary dimensions.

Findings

Developed a dynamic scheme based on T-matrix spectral density equations.

Generalized the off-shell-Jost function method for complex potentials.

Established a universal renormalization procedure for singular and nonlocal potentials.

Abstract

A dynamic scheme basing on equation for T-matrix momentum transfer spectral density and integral representation for Jost function is proposed for local Dirac Hamiltonians in arbitrary N- dimension spaces and for Schrodinger one with singular or nonlocal generalized Yukawa-type potentials. A generalization of the off-shell-Jost function method for that Hamiltonians and universal renormalization procedure of Jost function calculation for singular and nonlocal potentials is proposed.