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

• URL: http://arxiv.org/abs/2506.21400v1
• Date: Thu, 26 Jun 2025 15:47:39 GMT
• Title: Ghost-Free Quantisation of Higher Time-Derivative Theories via Non-Unitary Similarity Transformations
• Authors: Andreas Fring, Takano Taira, Bethan Turner,
• Abstract summary: We propose a novel method that preserves the bounded nature of the spectrum in one particular sector while restoring normalisability.<n>Inspired by techniques from pseudo/quasi-Hermitian PT-symmetric quantum mechanics, we construct a non-unitary map between two Hermitian Hamiltonians.<n>We show that the transformed system admits normalisable eigenstates and a spectrum bounded from below.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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