Classical fields method for a relativistic interacting Bose gas

We formulate a classical fields method for the description of relativistic interacting bosonic particles at nonzero temperatures. The method relies on the assumption that at low temperatures the Bose field can be described by a c-number function. We discuss a very important role of the cutoff momentum which divides the field into a dominant classical part and a small quantum correction. We illustrate the method by studying the thermodynamics of a relativistic Bose field which is governed by the Klein-Gordon equation with a lambda psi(4) term responsible for the interactions.