Wave Function of the Universe from a Matrix Valued First-Order Formalism

Abstract

In this paper, the Wheeler-DeWitt equation in full superspace formalism will be written in a matrix valued first-order formalism. We will also analyse the Wheeler-DeWitt equation in minisuperspace approximation using this matrix valued first-order formalism. We will note that this Wheeler-DeWitt equation, in this minisuperspace approximation, can be expressed as an eigenvalue equation. We will use this fact to analyse the spacetime foam in this formalism. This will be done by constructing a statistical mechanical partition function for the Wheeler-DeWitt equation in this matrix valued first-order formalism. This will lead to a possible solution for the cosmological constant problem.