LSZ ghostbusters in the quadratic gravity stage

TL;DR

This paper applies LSZ reduction and quantization methods to quadratic gravity, specifically Stelle gravity, addressing ghost states and deriving consistent rules despite non-standard algebra, with implications for ghost management.

Contribution

It derives LSZ rules within a non-standard oscillator algebra framework for quadratic gravity, providing a clearer approach to handling ghost states.

Findings

LSZ rules can be adapted to quadratic gravity with non-standard algebra

A simpler hermitian approach to negative norm states is developed

Results align with previous ghost management theories in quantum gravity

Abstract

The present letter considers the quantization method developed in [1]-[9], 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 [10]} and Pauli \[11]. However, taking into account the non standard oscillator algebra inherent to this method, 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 [12]-[13]. 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.