Phase Transition in Light-Front $\phi^4_{1+1}$

TL;DR

This paper demonstrates how light-front quantization with higher-derivative regularization reproduces the phase transition in $\,\phi^4_{1+1}$ theory, linking it to tachyonic modes and offering a new approach to compute critical couplings.

Contribution

It introduces a regularization method with higher derivatives in light-front quantization that naturally handles ultraviolet divergences without finite system size assumptions.

Findings

Reproduction of Chang's duality condition in the regularized theory

Identification of tachyons as related to phase transition

Potential for calculating critical coupling values

Abstract

We reproduce Chang's duality condition in a regularized $\phi^4_{1+1}$ theory quantized on a light front. The regularization involves higher derivatives in the Lagrangian, renders the model finite in the ultraviolet, and does not require introduction of a finite size of the system. It is demonstrated that the light-front quantization is a natural way to treat systems with higher derivatives. The phase transition is related to the presence of tachyons in the regularized theory. Prospects for computing the critical coupling in this formulation are briefly discussed.