Two-dimensional model of interaction of a non-relativistic particle with scalar mesons in the strong coupling limit

Bogolyubov transformations are introduced into the nonrelativistic model of particle interaction with scalar mesons. Within the framework of the generalized Hamiltonian formalism developed by Dirac, a translation-invariant perturbation theory in inverse powers of the coupling constant is constructed. Transmission and reflection coefficients are obtained, the S-matrix is written in a holomorphic representation, and the matrix element is calculated.