Ghost-free scalar-fermion interactions

Understand

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.