Lsz ghostbusters in the quadratic gravity stage

Abstract The present letter considers the quantization method developed in (Salvio et al. in Eur Phys J C 78(10):842, 2018; Salvio in Front Phys 6:77, 2018, Phys. Rev. D 99(10):103507, 2019, JCAP 09:027, 2022, JCAP 07:092, 2024, Salvio and Strumia in Eur Phys J C 76:227, 2016; Salvio and Strumia in JHEP 06:080, 2014, Eur Phys J C 78(2):124, 2018; Salvio and Veermae in JCAP 02:018, 2020), which postulates that, in several situations, negative norm or ghost states can be avoided in order to give positive probabilities. These authors also postulate a candidate for a path integral for those theories, following pioneer works initiated by Dirac (Proc R Soc Lond Ser A Math Phys Sci 180(980):1–40, 1942) and Pauli (Rev Mod Phys 15:175, 1943). It is of interest the derivation of the LSZ rules in this context, since it may not be clear at first sight that has the usual form of the textbooks, due to the non standard oscillator algebra and the redefinitions of the states. This is done here, applied to Stelle gravity (Phys Rev D 16:953, 1977, Gen Relativ Gravit 9:353, 1978). In addition, an equivalent but simpler way to deal with negative norm states is worked out, in which hermiticity is more explicit. As far as we understand, our conclusions fully agree with the arguments and expectations of those authors.