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

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.

12 pages, Latex, updated version

References in corpus (9)

• Avoiding Dark Energy with 1/R Modifications of Gravity
• No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model
• Third order equations of motion and the Ostrogradsky instability
• Instabilities in Metric-Affine Theories of Gravity
• (2+1)D Exotic Newton-Hooke Symmetry, Duality and Projective Phase
• A Chern-Simons approach to Galilean quantum gravity in 2+1 dimensions
• Canonical Structure of Higher Derivative Gravity in 3D
• Super-Planckian excursions of the inflaton and quantum corrections
• Ghost from constraints: a generalization of Ostrogradsky theorem