Equivalence of Many-Gluon Green's Functions in the Duffin–Kemmer–Petieu and Klein–Gordon–Fock Statistical Quantum Field Theories

We prove the equivalence of many-gluon Green's functions in the Duffin–Kemmer–Petieu and Klein–Gordon–Fock statistical quantum field theories. The proof is based on the functional integral formulation for the statistical generating functional in a finite-temperature quantum field theory. As an illustration, we calculate one-loop polarization operators in both theories and show that their expressions indeed coincide.