Spontaneous symmetry breaking in light front field theory

TL;DR

This paper develops a semiclassical framework for understanding spontaneous symmetry breaking in light front field theory, using finite-volume quantization and boundary conditions to analyze vacuum states and symmetry properties.

Contribution

It introduces a novel approach to spontaneous symmetry breaking in light front field theory by employing antiperiodic boundary conditions and unitary operators to define non-invariant vacuum states.

Findings

Vacuum states can be shifted to coherent states with lower energy.

Spontaneous symmetry breaking occurs in 2D b4 and 3D O(2) models.

Goldstone theorem is derived for the sigma model.

Abstract

A semiclassical picture of spontaneous symmetry breaking in light front field theory is formulated. It is based on a finite-volume quantization of self-interacting scalar fields obeying antiperiodic boundary conditions. This choice avoids a necessity to solve the zero mode constraint and enables one to define unitary operators which shift scalar field by a constant. The operators simultaneously transform the light-front vacuum to coherent states with lower energy than the Fock vacuum and with non-zero expectation value of the scalar field. The new vacuum states are non-invariant under the discrete or continuous symmetry of the Hamiltonian. Spontaneous symmetry breaking is described in this way in the two-dimensional \lambda\phi^4 theory and in the three-dimensional O(2)-symmetric sigma model. A qualitative treatment of topological kink solutions in the first model and a derivation of the Goldstone theorem in the second one is given. Symmetry breaking in the case of periodic boundary conditions is also briefly discussed.