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arXiv · 2104.01826

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

Biswajit Paul·Himangshu Dhar·Biswajit Saha
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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.

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Biswajit Paul, Himangshu Dhar, Biswajit Saha. 2021-04-05. Removal of instabilities of the higher derivative theories in the light of antilinearity. https://doi.org/10.1140/epjc%2Fs10052-021-09553-3

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