Higher-Derivative Massive Fermion Theories

TL;DR

This paper introduces a generalized two-dimensional massive fermion theory with higher derivatives, providing a canonical quantization, bosonization, and solutions for interacting models, advancing understanding of fermionic quantum field theories.

Contribution

It presents a novel higher-derivative fermion theory with derivative couplings, quantization, and bosonization, extending the framework of two-dimensional fermionic models.

Findings

Quantum solution expressed in terms of three fermions

Derived equivalent boson theory via bosonization

Solved a current-current interaction model

Abstract

We propose and canonically quantize a generalization of the two-dimensional massive fermion theory described by a Lagrangian containing third-order derivatives. In our approach the mass term contains a derivative coupling. The quantum solution is expressed in terms of three usual fermions. Employing the standard bosonization scheme, the equivalent boson theory is derived. The results obtained are used to solve a theory including a current-current interaction.