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This research advances fundamental quantum mechanics by applying covariant phase space formalism to resolve the Ostrogradsky ghost problem in higher-derivative theories like the Pais-Uhlenbeck oscillator. By successfully decoupling unphysical degrees of freedom through perturbation, the study provides a robust framework for quantizing systems that go beyond standard second-order dynamics. Such theoretical breakthroughs are essential for developing consistent models required by future quantum computing architectures and high-energy physics simulations.
Canonical quantization of the Pais-Uhlenbeck oscillator with a higher-derivative perturbation: a covariant phase space approach
arXiv:2608.00108v1 Announce Type: new Abstract: In this paper, we apply the covariant phase space formalism to the perturbative canonical quantization of the Pais-Uhlenbeck oscillator, with the acceleration-squared term treated as a perturbation. We quantize this model by constructing the symplectic form on the low-energy solution space. We then compute the energy spectrum and the unequal-time commutator in a perturbative way, and obtain the results that agree with the expansion of the exact low-energy theory. The perturbation method bypasses the standard Ostrogradsky construction and naturally decouples the Ostrogradsky ghost. This work extends our previous perturbative quantization scheme to genuine higher-derivative theories.
Abstract:In this paper, we apply the covariant phase space formalism to the perturbative canonical quantization of the Pais-Uhlenbeck oscillator, with the acceleration-squared term treated as a perturbation. We quantize this model by constructing the symplectic form on the low-energy solution space. We then compute the energy spectrum and the unequal-time commutator in a perturbative way, and obtain the results that agree with the expansion of the exact low-energy theory. The perturbation method bypasses the standard Ostrogradsky construction and naturally decouples the Ostrogradsky ghost. This work extends our previous perturbative quantization scheme to genuine higher-derivative theories.
arXiv:2608.00108 [quant-ph]
(or arXiv:2608.00108v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2608.00108 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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