The method of Ostrogradsky, quantization, and a move toward a ghost-free future

Abstract

The method of Ostrogradsky has been used to construct a first-order Lagrangian, hence Hamiltonian, for the fourth-order field-theoretical model of Pais–Uhlenbeck with unfortunate results when quantization is undertaken since states with negative norm, commonly called “ghosts,” appear. We propose an alternative route based on the preservation of symmetry and this leads to a ghost-free quantization.