Higher-Derivative Two-Dimensional Massive Fermion Theories

TL;DR

This paper investigates the quantization of higher-derivative two-dimensional massive fermion theories, revealing a spectrum of physical and unphysical excitations, and derives an equivalent bosonic theory to understand their properties.

Contribution

It introduces a canonical quantization framework for higher-derivative fermion theories, identifying physical and unphysical modes, and constructs an equivalent bosonized model.

Findings

Physical excitations include a massive fermion with positive metric.

Unphysical modes are massless fermions with opposite metrics.

The positive metric subspace is isolated by a subsidiary condition.

Abstract

We consider the canonical quantization of a generalized two-dimensional massive fermion theory containing higher odd-order derivatives. The requirements of Lorentz invariance, hermiticity of the Hamiltonian and absence of tachyon excitations suffice to fix the mass term, which contains a derivative coupling. We show that the basic quantum excitations of a higher-derivative theory of order 2N+1 consist of a physical usual massive fermion, quantized with positive metric, plus 2N unphysical massless fermions, quantized with opposite metrics. The positive metric Hilbert subspace, which is isomorphic to the space of states of a massive free fermion theory, is selected by a subsidiary-like condition. Employing the standard bosonization scheme, the equivalent boson theory is derived. The results obtained are used as a guideline to discuss the solution of a theory including a current-current interaction.