Multi-Time Version of the Landau-Peierls Formulation of Quantum Electrodynamics

TL;DR

This paper introduces a multi-time Schrödinger equation for quantum electrodynamics that improves upon the original Landau-Peierls formulation by being simpler, gauge-transparent, and Lorentz covariant, enhancing theoretical clarity.

Contribution

It presents a novel multi-time version of the Landau-Peierls quantum electrodynamics Hamiltonian, offering advantages in simplicity, gauge transparency, and Lorentz covariance.

Findings

Multi-time equations are simpler and more natural.

Equations are more transparent regarding gauge choices.

The formulation is manifestly Lorentz covariant.

Abstract

Landau and Peierls wrote down the Hamiltonian of a simplified version of quantum electrodynamics in the particle-position representation. We present a multi-time version of their Schr\"odinger equation, which bears several advantages over their original equation: the time evolution equations are simpler and more natural; they are more transparent with respect to choice of gauge; and, perhaps most importantly, they are manifestly Lorentz covariant. We discuss properties of the multi-time equations. Along the way, we also discuss the Lorentz covariant 3d Dirac delta distribution for spacelike surfaces and the inner product of photon wave functions on spacelike surfaces in an arbitrary gauge.