Novel Solution of Wheeler-DeWitt Theory

TL;DR

This paper introduces a novel analytical approach to the Wheeler-DeWitt quantum gravity theory by leveraging a global one-dimensionality conjecture, leading to new solutions and insights into wave functionals.

Contribution

It extends the global one-dimensionality conjecture to matter-dependent wave functionals and derives a solvable Dirac equation within the quantum gravity model.

Findings

Derived a Cauchy-like analytical wave functional for Wheeler-DeWitt theory.

Extended the conjecture to matter-dependent wave functionals.

Obtained and solved the Dirac equation in the quantum gravity context.

Abstract

Taking into account the global one-dimensionality conjecture recently proposed by the author, the Cauchy-like analytical wave functional of the Wheeler-DeWitt theory is derived. The crucial point of the integration strategy is canceling of the singular behavior of the effective potential, which is performed through the suitable change of variables introducing the invariant global dimension. In addition, the conjecture is extended onto the wave functionals dependent on both Matter felids as well as the invariant global dimension. Through application of the reduction within the quantum gravity model, the appropriate Dirac equation is obtained and than solved. The case of superposition is also briey discussed.