J an 2 00 1 Mass Generation of Nonlocal Field Theory

The possibility is investigated that a nonlocal formulation of gauge theories may provide an alternative mechanism for the generation of mass. For this purpose, a path-integral approach is used, with gauge-averaging term leading to an invertible integro-differential operator on field disturbances and to a mass term in the semiclassical Lagrangian. It is therefore shown that suitable choices of integral kernels make it possible to generate the mass of vector mesons from first principles (i.e. the need to obtain an invertible operator on field disturbances), without having to assume the existence of fundamental scalar fields which have not yet been observed. Although mass terms are not a generic property of nonlocal field theory, they can be therefore associated to an unavoidable step, i.e. the need to build invertible operators in perturbation theory. The paper proves also explicitly that the Faddeev–Popov procedure, when applied to a nonlocal gauge-averaging term, leads again to a BRST-invariant theory.