A Hamiltonian for Relativistic Interacting Many Particles

TL;DR

This paper derives an explicitly relativistic Hamiltonian for interacting many-particle systems by coupling particles with a scalar field, addressing a long-standing problem in relativistic quantum mechanics.

Contribution

It introduces a new Hamiltonian formulation for relativistic particles interacting via a scalar field, which reduces to known non-relativistic interactions.

Findings

Hamiltonian explicitly relativistic

Non-relativistic limit yields two-body interactions

Poincare algebra not fully satisfied due to time delay

Abstract

There is no relativistic Hamiltonian for many particles systems except for free particles and this has been accepted since the 1960s from the work of Currie, Jordan and Sudarshan, Cannon and Jordan, and Leutwyler. This is the problem we will address in this paper by coupling relativistic particles with a scalar field. The Hamiltonian we derive is explicitly relativistic and in the non-relativistic limit gives a Hamiltonian with two body interaction. However, we find that the Poincare algebra is still not satisfied because of the inherent time delayed interaction in relativistic particle systems.