  We introduce a classical field theory based on a concept of extended
causality that mimics the causality of a point-particle Classical Mechanics by
imposing constraints that are equivalent to a particle initial position and
velocity. It results on a description of discrete (pointwise) interactions in
terms of localized particle-like fields. We find the propagators of these
particle-like fields and discuss their physical meaning, properties and
consequences. They are conformally invariant, singularity-free, and describing
a manifestly covariant $(1+1)$-dimensional dynamics in a $(3+1)$ spacetime.
Remarkably this conformal symmetry remains even for the propagation of a
massive field in four spacetime dimensions. The standard formalism with its
distributed fields is retrieved in terms of spacetime average of the discrete
fields. Singularities are the by-products of the averaging proccess. This new
formalism enlightens the meaning and the problems of field theory, and may
allow a softer transition to a quantum theory.

High Energy Physics - Theory;High Energy Physics - Phenomenology