Canonical Transformations in a Higher-Derivative Field Theory

TL;DR

This paper constructs an exactly solvable two-dimensional higher-derivative fermionic quantum field theory with chiral-gauge invariance, using canonical transformations to relate it to standard Dirac spinors, and discusses its properties including Hamiltonian differences and correlation functions.

Contribution

It demonstrates the possibility of formulating a higher-derivative fermionic quantum field theory with chiral symmetry using canonical transformations, challenging previous beliefs.

Findings

Constructed an exactly solvable model with higher derivatives of even order.

Established a canonical transformation relating the model to Dirac spinors.

Analyzed the differences between original and transformed Hamiltonians.

Abstract

It has been suggested that the chiral symmetry can be implemented only in classical Lagrangians containing higher covariant derivatives of odd order. Contrary to this belief, it is shown that one can construct an exactly soluble two-dimensional higher-derivative fermionic quantum field theory containing only derivatives of even order whose classical Lagrangian exhibits chiral-gauge invariance. The original field solution is expressed in terms of usual Dirac spinors through a canonical transformation, whose generating function allows the determination of the new Hamiltonian. It is emphasized that the original and transformed Hamiltonians are different because the mapping from the old to the new canonical variables depends explicitly on time. The violation of cluster decomposition is discussed and the general Wightman functions satisfying the positive-definiteness condition are obtained.