90006927

open access

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S-matrix unitarity and renormalizability in higher-derivative theories

English (英語)

Progress of Theoretical and Experimental Physics

2019(8)

083B06-083B06

Oxford University Press (OUP)

2019-08

2020-03-17

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.

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