RADIATIVE-CORRECTIONS IN A NONLOCAL FIELD-THEORY

We extend the notion of a scalar field phi(x(mu)) to that of a field PHI(X(mu)(sigma)) so that the space-time point X(mu)(sigma) depends on a parameter sigma(0 less-than-or-equal-to sigma less-than-or-equal-to s). A straightforward generalization of the phi6(3) interaction is considered (viz: a PHI6(3) theory). Radiative corrections in both cases can be evaluated using a technique involving quantum mechanical path integrals. For the phi6(3) model, this involves the classical Lagrange density q2(tau)/2 (viz: that of a particle in the ''proper time gauge'') while for the PHI6(3) model the Lagrange density L = [Q2(sigma, tau)] - Q'2(sigma, tau)]/2 (viz: that of a string in the ''conformal gauge'') must be considered. The two-point function is examined in both cases.