$SQED_4$ and $QED_4$ on the null-plane

TL;DR

This paper analyzes scalar and spinor electrodynamics on the null-plane, detailing their constraint structures and deriving the fundamental brackets for quantization.

Contribution

It provides a comprehensive constraint analysis and quantization framework for $SQED_4$ and $QED_4$ in the null-plane formalism, including gauge fixing and boundary conditions.

Findings

Constraint structures are fully characterized.

Unique inverse of the second class constraint matrix obtained.

Generalized Dirac brackets derived for quantization.

Abstract

We studied the scalar electrodynamics ($SQED_{4}$) and the spinor electrodynamics ($QED_{4}$) in the null-plane formalism. We followed the Dirac's technique for constrained systems to perform a detailed analysis of the constraint structure in both theories. We imposed the appropriated boundary conditions on the fields to fix the hidden subset first class constraints which generate improper gauge transformations and obtain an unique inverse of the second class constraint matrix. Finally, choosing the null-plane gauge condition, we determined the generalized Dirac brackets of the independent dynamical variables which via the correspondence principle give the (anti)-commutators for posterior quantization.