New Approach to $N$-body Relativistic Quantum Mechanics

TL;DR

This paper introduces a novel self-consistent framework for relativistic quantum mechanics of many-body systems, bridging classical Newtonian and Schrödinger dynamics through nonlinear Dirac equations.

Contribution

It presents a new approach based on coupled nonlinear Dirac equations that unify classical and quantum many-body dynamics.

Findings

Classical limit reproduces Newtonian mechanics.

Nonrelativistic limit yields the Schrödinger equation.

Framework offers a unified description of many-body systems.

Abstract

In this paper, we propose a new approach to the relativistic quantum mechanics for many-body, which is a self-consistent system constructed by juxtaposed but mutually coupled nonlinear Dirac's equations. The classical approximation of this approach provides the exact Newtonian dynamics for many-body, and the nonrelativistic approximation gives the complete Schr\"odinger equation for many-body.