Bosonized Quantum Hamiltonian of the Two-Dimensional Derivative-Coupling Model

TL;DR

This paper derives the fully bosonized quantum Hamiltonian for the two-dimensional derivative-coupling model, revealing topological terms and quantum corrections that lead to a generalized Mandelstam soliton operator with continuous Lorentz spin.

Contribution

It provides the first detailed operator-based bosonization of the model, including quantum corrections and topological terms, resulting in a generalized soliton operator with continuous spin.

Findings

Quantum Hamiltonian includes topological terms with trivial equations of motion contributions.

Quantum corrections modify the bosonic equations of motion and the Fermi field's scale dimension.

Operator solution expressed via a generalized Mandelstam soliton operator with continuous Lorentz spin.

Abstract

Using the operator formulation we discuss the bosonization of the two-dimensional derivative-coupling model. The fully bosonized quantum Hamiltonian is obtained by computing the composite operators as the leading terms in the Wilson short distance expansion for the operator products at the same point. In addition, the quantum Hamiltonian contains topological terms which give trivial contributions to the equations of motion. Taking into account the quantum corrections to the bosonic equations of motion and to the scale dimension of the Fermi field operator, the operator solution is obtained in terms of a generalized Mandelstam soliton operator with continuous Lorentz spin (generalized statistics).