S$ -matrix unitarity and renormalizability in higher-derivative theories

Abstract We investigate the relation between $S$-matrix unitarity ($SS^\dagger=1$) and renormalizability in theories with negative-norm states. The relation has been confirmed in many field theories, including gauge theories and Einstein gravity, by analyzing the unitarity bound, which follows from...

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Bibliographic Details
Published inProgress of theoretical and experimental physics Vol. 2019; no. 8
Main Authors Abe, Yugo, Inami, Takeo, Izumi, Keisuke, Kitamura, Tomotaka, Noumi, Toshifumi
Format Journal Article
LanguageEnglish
Published Oxford University Press 01.08.2019
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Summary:Abstract We investigate the relation between $S$-matrix unitarity ($SS^\dagger=1$) and renormalizability in theories with negative-norm states. The relation has been confirmed in many field theories, including gauge theories and Einstein gravity, by analyzing the unitarity bound, which follows from the $S$-matrix unitarity and the norm positivity. On the other hand, renormalizable theories with a higher-derivative kinetic term do not necessarily satisfy the unitarity bound because of the negative-norm states. In these theories it is not known whether the $S$-matrix unitarity provides a nontrivial constraint related to the renormalizability. In this paper, by relaxing the assumption of norm positivity we derive a bound on scattering amplitudes weaker than the unitarity bound, which may be used as a consistency requirement for $S$-matrix unitarity. We demonstrate in scalar field models with a higher-derivative kinetic term that the weaker bound and the renormalizability imply identical constraints.
ISSN:2050-3911
2050-3911
DOI:10.1093/ptep/ptz084