A constructive approach to the quantum $(ch\varphi)_2$-model. I. The Gelfand–Levitan–Marcfaenko equations.method

Starting-from the quantum Gelfand–Levitan equations the quantum fields $\varphi_1$, and $\varphi_2$ are constructed which are the quantum analogs of $ch\varphi(x)$ and $sh\varphi(x)$ in the classical Sh-Gordon model. Wightman axioms including locality $PT$-invariance and asymptotic are completeness verified, and the scattering operator is calculated explicitly. In the developed approach no cut-offs are used and so renormalization effects do not appear. Bibl. – 15.