Critical Coupling in (1+1)-Dimensional Light-Front $\phi^{4}$ Theory. II -effects of non-diagonal interactionof non-diagonal interactions-

TL;DR

This paper investigates spontaneous symmetry breaking in (1+1)-dimensional light-front $^{4}$ theory, incorporating non-diagonal interactions to refine the critical coupling estimate and analyze parameter effects within the $$ expansion.

Contribution

It introduces a recalculation of commutation relations considering non-diagonal interactions and examines the impact of treating the coupling-to-mass ratio as an independent parameter.

Findings

Critical coupling consistent with equal-time results

Recalculated commutation relations with non-diagonal interactions

Analyzed effects of independent coupling-to-mass ratio

Abstract

Spontaneous symmetry breaking in (1+1)-dimensional $\phi^{4}$ theory is studied with discretized light-front quantization. Taking effects of non-diagonal interactions into account, the first few terms of the commutation relations $[a_{0},a_{n}]$ are recalculated in the $\hbar$ expansion. Our result of the critical coupling is still consistent with the equal-time result $22\mu^{2}/\hbar \le \lambda_{\rm{cr}} \le 55.5\mu^{2}/\hbar$. We also have examined effects of regarding the ratio of the bare coupling constant to a renormalized mass as an independent parameter in the $\hbar$ expansion.