Spontaneous symmetry breaking of (1+1)-dimensionalφ4theory in light-front field theory

We study spontaneous symmetry breaking in (1+1)-dimensional ${\phi }^4$ 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 ${\lambda }_{\mathrm{critical}}=4\mathrm{}\pi (3+\sqrt{3}){\mu }^2$, which is consistent with the value ${\lambda }_{\mathrm{critical}}=54.27\mathrm{}{\mu }^2$ 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 $\delta$ 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.