Solution to the Ghost Problem in Fourth Order Derivative Theories
Abstract
We present a solution to the ghost problem in fourth order derivative theories. In particular we study the PaisUhlenbeck 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 quantummechanical Hamiltonian and Hilbert space for the system. We find that while the secondquantized Fock space of the general PaisUhlenbeck 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 Smatrix 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 PaisUhlenbeck theory via path integration and by constructing the associated firstquantized wave mechanics, and show that the disappearance of the wouldbe 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 onshell 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.
 Publication:

Foundations of Physics
 Pub Date:
 May 2007
 DOI:
 10.1007/s1070100791197
 arXiv:
 arXiv:hepth/0608154
 Bibcode:
 2007FoPh...37..532M
 Keywords:

 higher derivative theories;
 ghosts;
 Pais&ndash;
 Uhlenbeck oscillator;
 High Energy Physics  Theory
 EPrint:
 36 pages, revtex. Prepared for the proceedings of the 2006 Biennial Meeting of the International Association for Relativistic Dynamics Version 2 contains an expanded discussion of the path integral quantization of the PaisUhlenbeck fourth order oscillator theory