Ghost-free scalar-fermion interactions

TL;DR

This paper develops a covariant framework for scalar-fermion interactions that avoids fermionic ghosts, ensuring correct degrees of freedom and proper evolution, with explicit examples and analysis of derivative interactions.

Contribution

It introduces a covariant theory for scalar-fermion interactions that evades fermionic ghosts and provides concrete conditions and examples for consistent dynamics.

Findings

Fermionic ghosts can be avoided in covariant scalar-fermion theories.

Explicit quadratic example with first derivatives demonstrates ghost-free conditions.

Derivative interaction terms cannot be eliminated by field redefinitions.

Abstract

We discuss a covariant extension of interactions between scalar fields and fermions in a flat space-time. We show, in a covariant theory, how to evade fermionic ghosts appearing because of the extra degrees of freedom behind a fermionic nature even in the Lagrangian with first derivatives. We will give a concrete example of a quadratic theory with up to the first derivative of multiple scalar fields and a Weyl fermion. We examine not only the maximally degenerate condition, which makes the number of degrees of freedom correct, but also a supplementary condition guaranteeing that the time evolution takes place properly. We also show that proposed derivative interaction terms between scalar fields and a Weyl fermion cannot be removed by field redefinitions.