An alternative Hamiltonian formulation for the Pais–Uhlenbeck oscillator

Ostrogradsky's method allows one to construct Hamiltonian formulation for a higher derivative system. An application of this approach to the Pais–Uhlenbeck oscillator yields the Hamiltonian which is unbounded from below. This leads to the ghost problem in quantum theory. In order to avoid this nasty feature, the technique previously developed in [7] is used to construct an alternative Hamiltonian formulation for the multidimensional Pais–Uhlenbeck oscillator of arbitrary even order with distinct frequencies of oscillation. This construction is also generalized to the case of an N=2N=2 supersymmetric Pais–Uhlenbeck oscillator.