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arXiv · 0807.1520

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

Aldo Déctor·Hugo A. Morales-Técotl·Luis F. Urrutia·J. David Vergara
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Abstract

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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Aldo Déctor, Hugo A. Morales-Técotl, Luis F. Urrutia, J. David Vergara. 2008-07-09. Coping with the Pais-Uhlenbeck oscillator's ghosts in a canonical approach. https://arxiv.org/abs/0807.1520

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