We introduce and study the four-dimensional analogue of a mass generation mechanism for non-Abelian gauge fields suggested in the paper, Phys. Lett. B 403, 297 (1997), in the case of three-dimensional space–time. The construction of the corresponding quantized theory is based on the fact that some nonlocal actions may generate local expressions for Green functions. An example of such a theory is the ordinary Yang–Mills field where the contribution of the Faddeev–Popov determinant to the Green functions can be made local by introducing additional ghost fields. We show that the quantized Hamiltonian for our theory unitarily acts in a Hilbert space of states and prove that the theory is renormalizable to all orders of perturbation theory. One-loop coupling constant and mass renormalizations are also calculated.
- Yang–Mills field
- mass generation