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

Bogolyubov transformations are introduced in the nonrelativistic model of the interaction of a particle with scalar mesons. A translationally invariant perturbation theory in reciprocal powers of the coupling constant is constructed in the framework of the generalized Hamiltonian formalism developed by Dirac. The transmission and reflection coefficients are obtained. The $S$ matrix is expressed in a holomorphic representation and the matrix elements are calculated.