Light-front Quantized Scalar Field Theory and Phase Transition

The light-front Hamiltonian formulation for the scalar field theory contains a new ingredient in the form of a constraint equation. Renormalization of the two dimensional $\phi^{4}$ theory, described in the continuum, is discussed. The mass renormalization condition and the renormalized constraint equation contain all the information to describe the phase transition in the theory, which is found to be of the second order. We argue that the same result would also be obtained in the conventional equal-time formulation.