Constraint equation and loop expansion in light-cone phi 4 field theory

Abstract

The constraint equation of the light-cone phi 4 field theory in 1+1 dimensions is the focus of the investigation of the non-triviality of the light-cone vacuum. The path-integral formalism developed from the Dirac-Bergmann algorithm is employed to calculate the vacuum expectation value instead of the constraint equation. The loop expansion given by Jackiw (1974) is used to calculate the effective potential as a function of the zero-mode field omega up to two-loop order. The minimum of the effective potential is at the vacuum expectation value of the phi field. A criterion for the first- or second-order phase transition is given by the effective potential and the critical coupling constants are calculated. Under the assumption that the zero and non-zero modes are classical fields, the constraint equation is used to solve for omega expressed in terms of the non-zero modes in a power series in h(cross). A static soliton solution for the non-zero modes is obtained from the constraint equation.