Regular Article - Theoretical Physics
Removal of instabilities of the higher derivative theories in the light of antilinearity
National Institute of Technology Agartala Jirania, 799 055, Tripura, India
Accepted: 16 August 2021
Published online: 26 August 2021
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 antilinearity 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 momentum 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.
© The Author(s) 2021
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