City Research Online

Abstract

We address the ghost problem in higher time-derivative theories (HTDTs) by reconsidering the sector that possesses a spectrum bounded from below but is usually dismissed due to non-normalisable states. We propose a novel method that restores normalisability in this sector by employing a non-unitary similarity transformation, while preserving the bounded nature of the spectrum. 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.

Publication Type:	Article
Additional Information:	Electronic version of an article published as International Journal of Modern Physics A https://doi.org/10.1142/S0217751X26501216 © copyright World Scientific Publishing Company https://www.worldscientific.com/worldscinet/ijmpa
Publisher Keywords:	Higher time-derivative theories, quantization
Subjects:	Q Science > QC Physics
Departments:	School of Science & Technology School of Science & Technology > Department of Mathematics
SWORD Depositor:	Symplectic Administrator

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