arXiv subjects

Himangshu Dhar

Publications and source records attributed to Himangshu Dhar.

3 recordsLinked to original sources

arXiv2021

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

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.

hep-th↗

arXiv2020

Ghosts in higher derivative Maxwell-Chern-Simon's theory and $\mathcal{PT}-$symmetry

Ghost fields in quantum field theory have been a long-standing problem. Specifically, theories with higher derivatives involve ghosts that appear in the Hamiltonian in the form of linear momenta term, which is commonly known as the Ostrogradski ghost. Higher derivative theories may involve both types of constraints i.e. first class and second class. Interestingly, these higher derivative theories may have non-Hermitian Hamiltonian respecting $\mathcal{PT}-$symmetries. In this paper, we have considered the $\mathcal{PT}-$symmetric nature of the extended Maxwell-Chern-Simon's theory and employed the second class constraints to remove the linear momenta terms causing the instabilities. We found that the removal is not complete rather conditions arise among the coefficients of the operator ${Q}$.

hep-th↗

arXiv2019

Treating Ostrogradski instability for Gallilean invariant Chern Simon's model via \mathcal{PT} symmetry

The Ostrogradski ghost problem that appears in higher derivative theories containing constraints has been considered here. Specifically we have considered systems where only the second class constraints appear. For these kind of systems, it is not possible to gauge away the linear momenta that cause the instability. To solve this issue, we have considered the PT symmetric aspects of the theory. As an example we have considered the Galilean invariant Chern Simons model in $2+1$ D which is a purely second class system. By solving the constraints, in the reduced phasespace, we have derived the \p similarity transformed Hamiltonian and putting conditions on we found that the final form of the Hamiltonian is free from any linear momenta and bounded from below.

hep-th↗