  The master field for a subclass of planar diagrams, so called rainbow
diagrams, for higher dimensional large N theories is considered. An explicit
representation for the master field in terms of noncommutative random variables
in the modified interaction representation in the Boltzmannian Fock space is
given. A natural interaction in the Boltzmannian Fock space is formulated by
means of a rational function of the interaction Lagrangian instead of the
ordinary exponential function in the standard Fock space.
