Hamiltonian Flow Equations for a Dirac Particle in an External Potential

TL;DR

This paper develops a method using Hamiltonian flow equations to transform and analyze a Dirac particle's Hamiltonian in an external potential, providing a systematic approach for simplifying complex quantum systems.

Contribution

It introduces a general procedure for applying continuous unitary transformations to Dirac Hamiltonians, enabling quasidiagonalization in external potentials.

Findings

Derived Hamiltonian flow equations for Dirac particles

Successfully reduced Hamiltonian to quasidiagonal form

Established a general method for continuous unitary transformations

Abstract

We derive and solve the Hamiltonian flow equations for a Dirac particle in an external static potential. The method shows a general procedure for the set up of continuous unitary transformations to reduce the Hamiltonian to a quasidiagonal form.