Gap Equations from Fermionic Constraints on the Light-Front

TL;DR

This paper explores how fermionic constraints, rather than zero-mode constraints, lead to gap equations in light-front four-Fermi theories, emphasizing the importance of infrared divergence treatment for symmetry breaking.

Contribution

It identifies fermionic constraints on nondynamical spinor components as the key to deriving gap equations in light-front formalism, offering a new perspective on symmetry breaking mechanisms.

Findings

Fermionic constraints replace zero-mode constraints in deriving gap equations.

Infrared divergence treatment is crucial for correct gap equation derivation.

Symmetry breaking is linked to fermionic constraints in light-front theories.

Abstract

We investigate how the gap equations are obtained in the light-front formalism within the four-Fermi theories. Instead of the zero-mode constraint, we find that the "fermionic constraints" on nondynamical spinor components are responsible for symmetry breaking. Careful treatment of the infrared divergence is indispensable for obtaining the gap equation.