Distribution Functions for Noncommuting Operators

The properties of a certain class of functions f(α^', β^', γ^', ⋯) of noncommuting observables α, β, γ, ⋯ are investigated. They have all the usual properties of distribution functions, except that they are complex. They satisfy simple Markoff-type stochastic equations and permit the calculation of the expectation values unambiguously. Conversely, quantum theory can be formulated in terms of such distribution functions having the prescribed properties.