Making sense of ghosts

TL;DR

This paper explores how ghost fields in quantum gravity can be understood within 0+1 dimensional quantum field theory, proposing methods to ensure unitarity and stability, and connecting to PT-symmetric quantum mechanics.

Contribution

It demonstrates that ghost theories can be made unitary and stable by constructing an appropriate inner product, and provides numerical analysis of spectra and wave functions.

Findings

Ghost theories are intrinsically unitary and perturbatively stable.

Nonperturbative stability can occur even when normal theories are unstable.

Numerical spectra and wave functions show violation of normal parity.

Abstract

Ghosts have been a stumbling block in the development of a UV complete quantum field theory for gravity. We discuss how difficulties associated with ghosts are overcome in the context of 0+1d QFT. Obtaining a probability interpretation is the key issue, and for this we discuss how an appropriate inner product can be constructed to define a sensible Born rule. Ghost theories are intrinsically unitary and perturbatively stable. They can also display nonperburbative stability even when the corresponding normal theory does not. The spectra and propagators are numerically obtained at both weak and strong coupling. Normalizable wave functions are obtained for the energy eigenstates and they show a violation of normal parity. We discuss connections to PT-symmetric quantum mechanics.