A Generalized Wick Transform for Gravity

TL;DR

This paper introduces a generalized Wick transform that maps Riemannian gravity constraints to Lorentzian ones, enabling a real-variable approach that simplifies canonical quantization.

Contribution

It presents a new generalized Wick transform based on Thiemann's observation, facilitating a real-variable formulation of quantum gravity including matter sources.

Findings

Transform successfully maps Riemannian to Lorentzian constraints

Enables work with real variables throughout the theory

Potentially simplifies the canonical quantization process

Abstract

Using a key observation due to Thiemann, a generalized Wick transform is introduced to map the constraint functionals of Riemannian general relativity to those of the Lorentzian theory, including matter sources. This opens up a new avenue within ``connection-dynamics'' where one can work, throughout, only with real variables. The resulting quantum theory would then be free of complicated reality conditions. Ramifications of this development to the canonical quantization program are discussed.