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

Abstract

The spontaneous symmetry breaking in (1+1)-dimensional $ϕ^{4}$ 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 $28.8μ^{2}/\hbar \le λ_{cr} \le 31.1μ^{2}/\hbar$ consistent with the equal-time one $22μ^{2}/\hbar \le λ_{cr} \le 55.5μ^{2}/\hbar$. The same analysis is also made under another operator ordering.