Chiral Condensates in the Light-Cone Vacuum

TL;DR

This paper develops a method to define meaningful order parameters for chiral symmetry breaking in light-cone quantization, overcoming the limitations of the traditional vacuum expectation values.

Contribution

It introduces a way to compute chiral condensates as expectation values of Heisenberg operators in the light-cone framework, enabling analysis of spontaneous symmetry breaking.

Findings

Derived gap equations for the models.

Calculated chiral condensate values.

Demonstrated spontaneous chiral symmetry breaking.

Abstract

In light-cone quantization, the standard procedure to characterize the phases of a system by appropriate ground state expectation values fails. The light-cone vacuum is determined kinematically. We show that meaningful quantities which can serve as order parameters are obtained as expectation values of Heisenberg operators in the equal (light-cone) time limit. These quantities differ from the purely kinematical expectation values of the corresponding Schroedinger operators. For the Nambu--Jona-Lasinio and the Gross-Neveu model, we describe the spontaneous breakdown of chiral symmetry; we derive within light-cone quantization the corresponding gap equations and the values of the chiral condensate.