Light-front Quantized Scalar Field Theory and Phase Transition

TL;DR

This paper explores the phase transition in two-dimensional scalar  theory using light-front Hamiltonian formulation, highlighting the role of a new constraint equation and renormalization in understanding second-order phase transitions.

Contribution

It introduces a novel constraint equation in light-front scalar field theory and demonstrates how renormalization captures the second-order phase transition, aligning with conventional formulations.

Findings

Phase transition is of second order.

Renormalization conditions fully describe the phase transition.

Results are consistent with equal-time formulation.

Abstract

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.