On The Symplectic Two-Form of Gravity in Terms of Dirac Eigenvalues

TL;DR

This paper explores the theoretical possibility of expressing the symplectic two-form in Euclidean gravity using Dirac eigenvalues, highlighting the formal solutions of the underlying equations.

Contribution

It investigates the formal relationship between the symplectic form and Dirac eigenvalues in Euclidean gravity, proposing a potential framework for their connection.

Findings

Existence of formal solutions for the symplectic form components

Potential to express the symplectic form in terms of Dirac eigenvalues

Theoretical framework for observables in Euclidean gravity

Abstract

The Dirac eigenvalues form a subset of observables of the Euclidean gravity. The symplectic two-form in the covariant phase space could be expressed, in principle, in terms of the Dirac eigenvalues. We discuss the existence of the formal solution of the equations defining the components of the symplectic form in this framework.