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Our purpose in this paper is to analyze the Pais-Uhlenbeck (PU) oscillatorusing complex canonical transformations. We show that starting from aLagrangian approach we obtain a transformation that makes the extended PUoscillator, with unequal frequencies, to be equivalent to two standard secondorder oscillators which have the original number of degrees of freedom. Suchextension is provided by adding a total time derivative to the PU Lagrangiantogether with a complexification of the original variables further subjected toreality conditions in order to maintain the required number of degrees offreedom. The analysis is accomplished at both the classical and quantum levels.Remarkably, at the quantum level the negative norm states are eliminated, aswell as the problems of unbounded below energy and non-unitary time evolution.We illustrate the idea of our approach by eliminating the negative norm statesin a complex oscillator. Next, we extend the procedure to the Pais-Uhlenbeckoscillator. The corresponding quantum propagators are calculated usingSchwinger's quantum action principle. We also discuss the equal frequency caseat the classical level.

An Alternative Canonical Approach to the Ghost Problem in a Complexified Extension of the Pais-Uhlenbeck Oscillator