Relativistic Hamiltonians in many-body theories

TL;DR

This paper explores the use of relativistic Hamiltonians in many-body nuclear systems, employing the Foldy-Wouthuysen transformation to connect field theory with relativistic potentials, and applies it to nuclear matter.

Contribution

It introduces a formalism that maps interacting nucleon-meson field theories to relativistic potentials expanded in 1/m_N, bridging relativistic mean field theory with many-body approaches.

Findings

Relativistic Hamiltonians effectively describe nuclear matter over various densities.

The formalism recovers relativistic mean field results in the Hartree approximation.

The approach provides a systematic way to include relativistic corrections in many-body nuclear models.

Abstract

We discuss the description of a many-body nuclear system using Hamiltonians that contain the nucleon relativistic kinetic energy and potentials with relativistic corrections. Through the Foldy-Wouthuysen transformation, the field theoretical problem of interacting nucleons and mesons is mapped to an equivalent one in terms of relativistic potentials, which are then expanded at some order in 1/m_N. The formalism is applied to the Hartree problem in nuclear matter, showing how the results of the relativistic mean field theory can be recovered over a wide range of densities.