The Causal Phase in $QED_{3}$

TL;DR

This paper determines the causal phase in (2+1)-dimensional QED, showing it can be constructed without ultraviolet divergences, contrasting with traditional approaches, and clarifies the scattering process in external electromagnetic fields.

Contribution

It explicitly computes the causal phase in (2+1)-dimensional QED using causality, avoiding ultraviolet divergences present in standard formulations.

Findings

No ultraviolet divergences in the causal phase construction.

Explicit determination of the phase from causality.

Contrast with usual QED formalism showing improved behavior.

Abstract

The operator ${\bf S}$ in Fock space which describes the scattering and particle production processes in an external time-dependent electromagnetic potential $A$ can be constructed from the one-particle S-matrix up to a physical phase $\lambda [A]$. In this work we determine this phase for $QED$ in (2+1) dimensions, by means of causality, and show that no ultraviolet divergences arise, in contrast to the usual formalism of $QED$.