Fermion Condensates and the Trivial Vacuum of Light-Cone Quantum Field Theory

TL;DR

This paper explores how to define fermionic condensates in light-cone quantum field theory, proposing methods to extract vacuum properties from particle spectra due to the trivial vacuum state.

Contribution

It introduces a framework for defining fermionic condensates in light-cone QFT and examines their relation to chiral symmetry breaking using models like 't Hooft and Schwinger.

Findings

Fermionic condensates can be inferred from the particle spectrum in light-cone QFT.

The Gell-Mann-Oakes-Renner relation is adapted to light-cone models.

The approach is illustrated with the 't Hooft and Schwinger models.

Abstract

We discuss the definition of condensates within light-cone quantum field theory. As the vacuum state in this formulation is trivial, we suggest to abstract vacuum properties from the particle spectrum. The latter can in principle be calculated by solving the eigenvalue problem of the light-cone Hamiltonian. We focus on fermionic condensates which are order parameters of chiral symmetry breaking. As a paradigm identity we use the Gell-Mann-Oakes-Renner relation between the quark condensate and the observable pion mass. We examine the analogues of this relation in the `t~Hooft and Schwinger model, respectively. A brief discussion of the Nambu-Jona-Lasinio model is added.