Spontaneous symmetry breaking of (1+1)-dimensional phi4 theory in light-front field theory.

Abstract

We study spontaneous symmetry breaking in (1+1)-dimensional ${\ensuremath{\varphi}}^{4}$ theory using the light-front formulation of 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 ${\ensuremath{\lambda}}_{\mathrm{critical}}=4\ensuremath{\pi}(3+\sqrt{3}){\ensuremath{\mu}}^{2}$, which is consistent with the value ${\ensuremath{\lambda}}_{\mathrm{critical}}=54.27{\ensuremath{\mu}}^{2}$ obtained in the equal-time theory. We calculate the vacuum expectation value as a function of the coupling constant in the broken phase both numerically and analytically using the $\ensuremath{\delta}$ expansion. We find two equivalent broken phases. Finally we show that the energy levels of the system have the expected behavior for the broken phase.