Quantum field theory in the infinite temperature limit

The T = infinity limit for renormalizable 4-dimensional Euclidean QFT is considered. A general arguement is presented in three examples: phi3, QED, QCD. Using an expansion of the Green's functions generating functional, it is shown at T = infinity quantum dynamics generally becomes 3 dimensional. All superficially divergent diagrams survive at T = infinity and ensure renormalization of effective dynamics. The correction to naive dimensional reduction is studied; appearance of ''electric'' masses in QED and QCD is shown to be the result of such a correction. A curious symmetry of the generating functional in QED and QCD, its implications and breaking by the thermal corrections of heavy modes are discussed. Presence of the symmetry implies survival of some fermion modes at T = infinity