  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.
