Boson field description of fermions in two dimensions

It is shown that any interacting spinor system in two dimensions can be equivalently described by the scalar system. The equivalency is complete in the sense that both theories have the common Hamiltonian. In the solvable case like the massless Thirring model, the scalar field version of the Hamiltonian is bilinear on the field variables. It becomes of the standard form of the free Hamiltonian by the suitable choice of the field variables. The spinor field version of the Hamiltonian also becomes of the standard form of the free Hamiltonian by the corresponding choice of the field variables. The canonical Hamiltonian in the spinor version does not necessarily satisfy the integrability condition. Then the use of the integrable Hamiltonian is the essential point in this paper. The vector-meson system is also describable by the scalar system. (auth.)