Investigation on theories with pt symmetry for removal of the ostrogradski ghosts

Abstract

Since the beginning, the higher-derivative theories are suffering newlinefrom a problem called the Ostrogradski ghost problem. If the Hamiltonian newlineis non-Hermitian by nature, it leads to a negative energy spectrum newlinewhich therefore violates the unitarity. But if the non-Hermitian newlineHamiltonian possesses PT -symmetry the Hamiltonian turned into newlineHermitian, which governs the system to lead to the real energy eigen newlinevalues, which in turn thus preserves the probability of the system. newlineWe have taken the higher derivative theories which can be made newlinenon-Hermitian by proper similarity transformation and considered the newlinePT -symmetric attributes to remove the Ostrogradski instabilities. newline