Asymptotic States and the Definition of the S-matrix in Quantum Gravity

TL;DR

This paper develops a framework for defining the S-matrix in quantum gravity by using a gauge theory of volume-preserving diffeomorphisms, introducing a gravitational limit, and establishing LSZ reduction formulae for observable particles.

Contribution

It introduces a novel approach to quantum gravity by defining the S-matrix through a gravitational limit within a gauge theory, extending LSZ reduction to this context.

Findings

Defined the gravitational limit mapping gravitational to inertial energy-momentum.

Constructed Fock spaces for asymptotic states in quantum gravity.

Established LSZ reduction formulae for gravitationally interacting fields.

Abstract

Viewing gravitational energy-momentum as equal by observation, but different in essence from inertial energy-momentum naturally leads to the gauge theory of volume-preserving diffeormorphisms of an inner Minkowski space. The generalized asymptotic free scalar, Dirac and gauge fields in that theory are canonically quantized, the Fock spaces of stationary states are constructed and the gravitational limit - mapping the gravitational energy-momentum onto the inertial energy-momentum to account for their observed equality - is introduced. Next the S-matrix in quantum gravity is defined as the gravitational limit of the transition amplitudes of asymptotic in- to out-states in the gauge theory of volume-preserving diffeormorphisms. The so defined S-matrix relates in- and out-states of observable particles carrying gravitational equal to inertial energy-momentum. Finally generalized LSZ reduction formulae for scalar, Dirac and gauge fields are established which allow to express S-matrix elements as the gravitational limit of truncated Fourier-transformed vacuum expectation values of time-ordered products of field operators of the interacting theory. Together with the generating functional of the latter established in an earlier paper [8] any transition amplitude can in principle be computed to any order in perturbative quantum gravity.