Perturbative Approach to Higher Derivative Theories with Fermions

TL;DR

This paper develops a perturbative method to handle higher derivative terms in theories with fermions, deriving effective Lagrangians and analyzing implications for Hamiltonian stability, mass, and vacuum structure.

Contribution

It extends a perturbative approach to include fermionic higher derivative theories, providing a systematic way to obtain effective first-order Lagrangians and analyze their physical properties.

Findings

Effective Lagrangian with only first derivatives derived

Hamiltonian bounded from below at first order for potentials

Higher derivatives induce effective mass and vacuum changes

Abstract

We extend the perturbative approach developed in an earlier work to deal with Lagrangians which have arbitrary higher order time derivative terms for both bosons and fermions. This approach enables us to find an effective Lagrangian with only first time derivatives order by order in the coupling constant. As in the pure bosonic case, to the first order, the quantized Hamiltonian is bounded from below whenever the potential is. We show in the example of a single complex fermion that higher derivative interactions result in an effective mass and change of vacuum for the low energy modes. The supersymmetric noncommutative Wess-Zumino model is considered as another example. We also comment on the higher derivative terms in Witten's string field theory and the effectiveness of level truncation.