Noncovariant gauge fixing in the quantum Dirac field theory of atoms and molecules

TL;DR

This paper extends quantum electrodynamics to include noncovariant gauge fixing, enabling a Hamiltonian formulation suitable for describing atoms and molecules with a relativistic Dirac field, highlighting gauge freedom implications.

Contribution

It introduces a gauge fixing formalism in QED that incorporates noncovariant gauges, providing a new Hamiltonian framework for atomic and molecular relativistic quantum theory.

Findings

Derived Hamiltonian suitable for atoms and molecules

Established gauge choices including Coulomb and Poincaré gauges

Discussed implications of gauge freedom in noncovariant QED

Abstract

Starting from the Weyl gauge formulation of quantum electrodynamics (QED), the formalism of quantum-mechanical gauge fixing is extended using techniques from nonrelativistic QED. This involves expressing the redundant gauge degrees of freedom through an arbitrary functional of the gauge-invariant transverse degrees of freedom. Particular choices of functional can be made to yield the Coulomb gauge and Poincar\'{e} gauge representations. The Hamiltonian we derive therefore serves as a good starting point for the description of atoms and molecules by means of a relativistic Dirac field. We discuss important implications for the ontology of noncovariant canonical QED due to the gauge freedom that remains present in our formulation.