Removal of instabilities of the higher derivative theories in the light of antilinearity
arXiv:2104.01826 · doi:10.1140/epjc/s10052-021-09553-3
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 -operator, which acts as an intertwining operator between the Hamiltonian and its hermitian conjugate. We have used this -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.
arXiv comment12 pages, Latex, updated version
References in corpus (32)
- Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
- f(R) Theories Of Gravity
- Complex Extension of Quantum Mechanics
- Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability
- Avoiding Dark Energy with 1/R Modifications of Gravity
- Introduction to PT-Symmetric Quantum Theory
- No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model
- Extension of PT-Symmetric Quantum Mechanics to Quantum Field Theory with Cubic Interaction
- Cosmological and black hole brane-world Universes in higher derivative gravity
- Galilean-Invariant (2+1)-Dimensional Models with a Chern-Simons-Like Term and D=2 N oncommutative Geometry
- Higher derivative theories with constraints : Exorcising Ostrogradski's Ghost
- A new PT symmetric complex Hamiltonian with a real spectra
- Third order equations of motion and the Ostrogradsky instability
- Ghosts in metric-affine higher order curvature gravity
- Leading higher-derivative corrections to Kerr geometry
- Consistency of Higher Derivative Gravity in the Brane Background
- Anyon wave equations and the noncommutative plane
- Instabilities in Metric-Affine Theories of Gravity
- Calculation of the Hidden Symmetry Operator in PT-Symmetric Quantum Mechanics
- (2+1)D Exotic Newton-Hooke Symmetry, Duality and Projective Phase
- Exorcising the Ostrogradsky ghost in coupled systems
- A Chern-Simons approach to Galilean quantum gravity in 2+1 dimensions
- Ghost-free theories with arbitrary higher-order time derivatives
- Higher-order modified Starobinsky inflation
- Canonical Structure of Higher Derivative Gravity in 3D
- Super-Planckian excursions of the inflaton and quantum corrections
- On the higher-derivative supersymmetric gauge theory
- Appropriate Inner Product for PT-Symmetric Hamiltonians
- Fractal geometry of higher derivative gravity
- Removing Ostrogradski ghost from degenerate gravity theories
- Ghost from constraints: a generalization of Ostrogradsky theorem
- Treating Ostrogradski instability for Gallilean invariant Chern Simon's model via \mathcal{PT} symmetry