Critical coupling in (1+1)-dimensional light-front $\phi^{4}$ theory

TL;DR

This paper investigates the critical coupling for spontaneous symmetry breaking in (1+1)-dimensional light-front $^{4}$ theory using discretized light-front quantization and zero-mode constraints, providing results consistent with equal-time quantization.

Contribution

It introduces a method to evaluate the critical coupling in light-front $^{4}$ theory via zero-mode analysis and compares different operator orderings.

Findings

Critical coupling range: 28.8 to 31.1 $rac{ ext{mu}^2}{ ext{hbar}}$

Consistent with equal-time results, 22 to 55.5 $rac{ ext{mu}^2}{ ext{hbar}}$

Zero-mode analysis supports spontaneous symmetry breaking understanding

Abstract

The spontaneous symmetry breaking in (1+1)-dimensional $\phi^{4}$ theory is studied with discretized light-front quantization, that is, by solving the zero-mode constraint equation. The symmetric ordering is assumed for the operator-valued constraint equation. The commutation relation between the zero mode and each oscillator mode is calculated with $\hbar$ expansion. A critical coupling evaluated from the first some terms in the expansion is $28.8\mu ^{2}/\hbar \le \lambda_{cr} \le 31.1\mu ^{2}/\hbar$ consistent with the equal-time one $22\mu ^{2}/\hbar \le \lambda_{cr} \le 55.5\mu ^{2}/\hbar$. The same analysis is also made under another operator ordering.