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.
Highlights
Construction of general theory without ghost degrees of freedom (d.o.f.) has been discussed for a long time
III, we concretely write down the quadratic theory of n-scalar and one Weyl fermion fields and apply the set of the maximally degenerate conditions, which we have proposed for removing the fermionic ghosts properly
As usually discussed in the Lagrangian composed of bosonic d.o.f., we have to avoid the appearance of ghosts even in boson-fermion coexisting Lagrangians
Summary
Construction of general theory without ghost degrees of freedom (d.o.f.) has been discussed for a long time. III to multiple Weyl fermions and derive the primary constraints
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