Coping with the Pais-Uhlenbeck oscillator's ghosts in a canonical approach

Details Coping with the Pais-Uhlenbeck oscillator's ghosts in a canonical approach Coping with the Pais-Uhlenbeck oscillator's ghosts in a canonical approach

2008-07-09

arxiv.org/abs/0807.1520v1

Physics

Quantum Physics

5 pages

Scientific paper

A {\em complex} canonical transformation is found that takes the fourth order derivative Pais-Uhlenbeck oscillator into two independent harmonic oscillators thus showing that this model has energy bounded from below, unitary time-evolution and no negative norm states, or ghosts. Such transformation yields a positive definite inner product consistent with reality conditions in the Hilbert space. The method is illustrated by eliminating the negative norm states in a complex oscillator. Extensions to other higher order mechanical models and field theory are discussed.

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