Investigations on a bi-chiral scalar field

TL;DR

This paper explores the quantum inconsistencies of a second order equation describing two same-chirality chiral boson fields in (1+1) dimensions, highlighting issues in formulating a consistent quantum theory.

Contribution

It clarifies the problems arising from second order equations for chiral bosons and emphasizes the importance of first order formulations for quantum consistency.

Findings

Second order equations lead to unacceptable quantum theories for chiral bosons.

First order equations are necessary for consistent quantum descriptions.

The study clarifies the classical-quantum relationship in chiral scalar fields.

Abstract

Chiral boson fields in (1+1) dimensions obey a first order equation of motion. A second order equation which classically describes two chiral boson fields of the same chirality leads, however, to an unacceptable quantum theory