Critical Coupling in (1+1)-Dimensional Light-Front ϕ4 Theory

The spontaneous symmetry breaking in (1+1)-dimensional $\phi^{4}$ theory isstudied with discretized light-front quantization, that is, by solving thezero-mode constraint equation. The symmetric ordering is assumed for theoperator-valued constraint equation. The commutation relation between the zeromode and each oscillator mode is calculated with $\hbar$ expansion. A criticalcoupling 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 theequal-time one $22\mu ^{2}/\hbar \le \lambda_{cr} \le 55.5\mu ^{2}/\hbar$. Thesame analysis is also made under another operator ordering