The Continuum Version of \phi^4_{1+1}-theory in Light-Front Quantization

TL;DR

This paper develops a mathematically rigorous continuum light-front quantization method for _{1+1}-theory, addressing divergences and renormalization, and compares critical coupling results with discretized approaches.

Contribution

It introduces a continuum operator distribution framework for _{1+1}-theory in light-front quantization, improving divergence handling and providing new critical coupling estimates.

Findings

Critical coupling increases by 30% compared to discretized methods.

RG improved calculations yield a critical coupling of approximately 1.8.

The continuum approach simplifies non-perturbative analysis without added complexity.

Abstract

A genuine continuum treatment of the massive \phi^4_{1+1}-theory in light-cone quantization is proposed. Fields are treated as operator valued distributions thereby leading to a mathematically well defined handling of ultraviolet and light cone induced infrared divergences and of their renormalization. Although non-perturbative the continuum light cone approach is no more complex than usual perturbation theory in lowest order. Relative to discretized light cone quantization, the critical coupling increases by 30% to a value r = 1.5. Conventional perturbation theory at the corresponding order yields r_1=1, whereas the RG improved fourth order result is r_4 = 1.8 +-0.05.