Nonlocal Form of Quantum Off-Shell Kinetic Equation

TL;DR

This paper introduces a new nonlocal form of the quantum off-shell kinetic equation that improves conservation laws and is suitable for numerical simulations of heavy-ion collisions.

Contribution

It derives a nonlocal kinetic equation form that enhances conservation accuracy and maintains applicability for test-particle numerical methods.

Findings

More accurate conservation of Noether quantities.

Equivalent to existing formulations within formal applicability.

Suitable for numerical simulation of heavy-ion collisions.

Abstract

A new nonlocal form of the off-shell kinetic equation is derived. While being equivalent to the Kadanoff--Baym and Botermans--Malfliet formulations in the range of formal applicability, it has certain advantages beyond this range. It possesses more accurate conservation laws for Noether quantities than those in the Botermans--Malfliet formulation. At the same time the nonlocal form, similarly to the Botermans--Malfliet one, allows application of the test-particle method for its numerical solution, which makes it practical for simulations of heavy-ion collisions. The physical meaning of the time-space nonlocality is clarified.