Generalised Wick Transform in Dimensionally Reduced Gravity

TL;DR

This paper explores a generalized Wick transform in dimensionally reduced quantum gravity, showing its equivalence to standard quantization and providing a method to derive Lorentzian physical states from Riemannian solutions.

Contribution

It introduces a generalized Wick transform scheme for symmetry-reduced models in quantum gravity, linking Riemannian and Lorentzian quantum theories.

Findings

The generalized Wick transform is equivalent to standard quantization in studied models.

Physical Lorentzian states can be obtained by Wick transforming Riemannian solutions.

The approach simplifies the connection between Riemannian and Lorentzian quantum gravity.

Abstract

In the context of canonical quantum gravity, we study an alternative real quantisation scheme, which is arising by relating simpler Riemannian quantum theory to the more complicated physical Lorentzian theory - the generalised Wick transform. On the symmetry reduced models, homogenous Bianchi cosmology and 2+1 gravity, we investigate its generalised construction principle, demonstrate that the emerging quantum theory is equivalent to the one obtained from standard quantisation and how to obtain physical states in Lorentzian gravity from Wick transforming solutions of Riemannian quantum theory.