Epstein-Glaser’s Causal Light-Front Field Theory

Abstract

Epstein-Glaser’s ideas for the formulation of a distributional well-defined perturbative causal field theory are developed in light-front dynamics over the invariant null-plane coordinates introduced by Rohrlich. Explicitly, the causality theorems which warrant the method are adapted to that dynamics, and the causal distribution splitting formulae are re-derived in accordance with it, exhibiting important differences with respect to its instant dynamics version. Application of these splitting formulae to the (anti)commutation relations of the fermion and radiation fields naturally leads to the well known instantaneous terms of their Feynman propagators, while the scalar field’s one retains its form from instant dynamics. Additionally, the developed method is applied to Scalar QED (SQED) at second order, taking for the first order distribution the product of the radiation field with only the linear in the coupling constant part of the current. We analyse Moeller scattering, for which the equivalence with instant dynamics is established, and Compton scattering, for which the vertex coming from the second order term in the current is automatically generated in the normalization procedure once the residual gauge invariance which remains from the imposition of the null-plane gauge condition is exploited.