Ghost-Free Quantisation of Higher Time-Derivative Theories via Non-Unitary Similarity Transformations
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| Format: | Preprint |
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2025
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| _version_ | 1866913914234601472 |
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| author | Fring, Andreas Taira, Takano Turner, Bethan |
| author_facet | Fring, Andreas Taira, Takano Turner, Bethan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_21400 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ghost-Free Quantisation of Higher Time-Derivative Theories via Non-Unitary Similarity Transformations Fring, Andreas Taira, Takano Turner, Bethan Quantum Physics High Energy Physics - Theory Mathematical Physics 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. |
| title | Ghost-Free Quantisation of Higher Time-Derivative Theories via Non-Unitary Similarity Transformations |
| topic | Quantum Physics High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2506.21400 |