  We present a solution to the ghost problem in fourth order derivative
theories. In particular we study the Pais-Uhlenbeck fourth order oscillator
model, a model which serves as a prototype for theories which are based on
second plus fourth order derivative actions. Via a Dirac constraint method
quantization we construct the appropriate quantum-mechanical Hamiltonian and
Hilbert space for the system. We find that while the second-quantized Fock
space of the general Pais-Uhlenbeck model does indeed contain the negative norm
energy eigenstates which are characteristic of higher derivative theories, in
the limit in which we switch off the second order action, such ghost states are
found to move off shell, with the spectrum of asymptotic in and out S-matrix
states of the pure fourth order theory which results being found to be
completely devoid of states with either negative energy or negative norm. We
confirm these results by quantizing the Pais-Uhlenbeck theory via path
integration and by constructing the associated first-quantized wave mechanics,
and show that the disappearance of the would-be ghosts from the energy
eigenspectrum in the pure fourth order limit is required by a hidden symmetry
that the pure fourth order theory is unexpectedly found to possess. The
occurrence of on-shell ghosts is thus seen not to be a shortcoming of pure
fourth order theories per se, but rather to be one which only arises when
fourth and second order theories are coupled to each other.
