  A class of interacting classical random fields is constructed using deformed
*-algebras of creation and annihilation operators. The fields constructed are
classical random field versions of "Lie fields". A vacuum vector is used to
construct linear forms over the algebras, which are conjectured to be states
over the algebras. Assuming this conjecture is true, the fields constructed are
"quantum random fields" in the sense that they have Poincare invariant vacua
with a fluctuation scale determined by Planck's constant. A nonlocal particle
interpretation of the formalism is shown to be the same as a particle
interpretation of a quantum field theory.
