Spontaneous Symmetry Breaking Mechanism in Light-Front Quantized Field Theory- (Discretized Formulation)

TL;DR

This paper investigates spontaneous symmetry breaking in light-front quantized scalar field theory using a discretized approach, revealing a non-local constraint and its implications for the Hamiltonian and phase stability.

Contribution

It introduces a non-local constraint in discretized light-front scalar field theory and analyzes its role in spontaneous symmetry breaking and phase instability.

Findings

Non-commuting background and non-zero mode variables at finite volume.

Derivation of a non-local constraint relating these variables.

Constraint influences the form of the light-front Hamiltonian and phase stability.

Abstract

The scalar field is quantized in the discretized light-front framework following the {\em standard} Dirac procedure and its infinite volume limit taken. The background field and the nonzero mode variables do not commute for finite volume; they do so only in the continuum limit. A {\em non-local constraint} in the theory relating the two is shown to follow and we must deal with it along with the Hamiltonian. At the tree level the constraint leads to a description of the spontaneous symmetry breaking. The elimination of the constraint would lead to a highly involved light-front Hamiltonian in contrast to the one found when we ignore altogether the background field. The renormalized constraint equation would also account for the instability of the symmetric phase for large enough couping constant.