Spontaneous Symmetry Breaking of phi4(1+1) in Light Front Field Theory

TL;DR

This paper investigates spontaneous symmetry breaking in 1+1 dimensional phi^4 theory using light-front quantization, finding critical coupling and vacuum expectation values consistent with equal-time results.

Contribution

It introduces a zero-mode solution approach in light-front field theory and demonstrates symmetry breaking with quantitative agreement to traditional methods.

Findings

Spontaneous symmetry breaking occurs at lambda_critical = 4 pi(3+sqrt 3).

Vacuum expectation value varies with coupling, confirming broken phases.

Energy levels behave as expected in the broken phase.

Abstract

We study spontaneous symmetry breaking in phi^4_(1+1) using the light-front formulation of the field theory. Since the physical vacuum is always the same as the perturbative vacuum in light-front field theory the fields must develop a vacuum expectation value through the zero-mode components of the field. We solve the nonlinear operator equation for the zero-mode in the one-mode approximation. We find that spontaneous symmetry breaking occurs at lambda_critical = 4 pi(3+sqrt 3), which is consistent with the value lambda_critical = 54.27 obtained in the equal time theory. We calculate the value of the vacuum expectation value as a function of the coupling constant in the broken phase both numerically and analytically using the delta expansion. We find two equivalent broken phases. Finally we show that the energy levels of the system have the expected behavior within the broken phase.