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

Abstract

The spontaneous symmetry breaking in (1+1)-dimensional ${\varphi }^4$ 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 $\hslash$ expansion. A critical coupling evaluated from the first some terms in the expansion is $28.8{\mu }^2/\hslash \le {\lambda }_{cr}\le 31.1{\mu }^2/\hslash$ consistent with the equal-time one $22{\mu }^2/\hslash \le {\lambda }_{cr}\le 55.5{\mu }^2/\hslash$. The same analysis is also made under another operator ordering.