  A method is developed to construct a non-local massless scalar field theory
in a flat quantised space-time generated by an operator algebra. Implicit in
the operator algebra is a fundamental length scale of the space-time. The
fundamental two-point function of free fields is constructed by assuming that
the causal Green functions still have support on the light cone in the operator
algebra quantised space-time. In contrast to previous stochastic approaches,
the method introduced here requires no explicit averaging over spacetime
coordinates. The two- and four-point functions of~$g \varphi^4$ theory are
calculated to the one-loop level, and no ultraviolet divergences are
encountered. It is also demonstrated that there are no IR divergences in the
processes considered.
