Fermionization of the $(\sin\varphi)_2$ interaction in a box

A scheme is proposed for the canonical quantization of the $(\sin\varphi)_2$ model in a finite spatial box. This scheme takes into account the basic specific features of the phase space of the classical model (the presence of topological charge, the existence of soliton solutions, multiplicity of the classical “vacuum” solutions, etc.). Boson canonical variables are introduced and used to construct correct fermion fields in the box that admit passage to infinite volume. A representation of the canonical anticommutation relations realized by the constructed fermion fields is described. The exact connection between the different boson and fermion physical quantities in the box is established.