Fermion Operator Ordering and the Quantum c-Number Correspondence

The linearly ordered and the exponentially ordered forms of an arbitrary spin $12$-Fermion operator are defined and evaluated. As an application an expression for $exp (αb̂) exp (βb̂†)$ is evaluated which resembles the usual Baker-Hausdorff identity. It is shown that the trace of the product of two Fermion operators can be expressed as a three-dimensional integral over c-number functions. Further the quantum equations of motion are also expressible as equations involving c-number functions.