Removal of instabilities of the higher derivative theories in the light of antilinearity

TL;DR

This paper proposes a novel method to eliminate instabilities in higher derivative theories by leveraging antilinearity in non-Hermitian Hamiltonians, using a V-operator to remove Ostrogradski ghosts through similarity transformations.

Contribution

It introduces a new approach to stabilize higher derivative theories by applying antilinearity and non-Hermitian Hamiltonian techniques, avoiding Ostrogradski ghosts.

Findings

Successfully removes linear instabilities in higher derivative Hamiltonians.

Uses V-operator to transform Hamiltonian into a ghost-free form.

Achieves stability under specific mass term restrictions.

Abstract

Theories with higher derivatives involve linear instabilities in the Hamiltonian commonly known as Ostrogradski ghosts and can be viewed as a very serious problem during quantization. To cure {this} , we have considered the properties of antilinearty that can be found inherently in the non-Hermitian Hamiltonians. Owing to the existence of antilinearity, we can construct an operator, called the $V$-operator, which acts as an intertwining operator between the Hamiltonian and its hermitian conjugate. We have used this $V$-operator to remove the linear momenta term from the higher derivative Hamiltonian by making it non-Hermitian in the first place via an isospectral similarity transformation. The final form of the Hamiltonian is free from the Ostrogradski ghosts under some restriction on the mass term.