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

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.