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arXiv · 2506.21400

Ghost-Free Quantisation of Higher Time-Derivative Theories via Non-Unitary Similarity Transformations

Andreas Fring·Takano Taira·Bethan Turner
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Abstract

We address the long-standing ``ghost problem" in higher time-derivative theories (HTDTs), where quantisation typically yields sectors with either unbounded spectra or non-normalisable eigenstates; both rendering the theory unphysical. We propose a novel method that preserves the bounded nature of the spectrum in one particular sector while restoring normalisability by employing a non-unitary similarity transformation. Inspired by techniques from pseudo/quasi-Hermitian PT-symmetric quantum mechanics, we construct a non-unitary map between two Hermitian Hamiltonians, converting ghostly sectors into physically viable ones. We demonstrate the feasibility of this approach using a concrete HTDT model, related to the Pais-Uhlenbeck oscillator, and show that the transformed system admits normalisable eigenstates and a spectrum bounded from below. This framework offers a consistent re-interpretation of HTDTs and extends the toolbox for constructing ghost-free quantum models.

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Andreas Fring, Takano Taira, Bethan Turner. 2025-06-26. Ghost-Free Quantisation of Higher Time-Derivative Theories via Non-Unitary Similarity Transformations. https://arxiv.org/abs/2506.21400

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