CAUSALITY REQUIREMENTS AND LINEAR FIELD EQUATIONS

Abstract

The requirements of Lorentz and time-reversal invariance, causality, positive definiteness of the field energy, and a boundedness condition on the propagator are used to determine the possible forms of linear field equations through the determination of their Green's functions in momentum space. The classical definition of causality, no output before input, is applied to a scalar field and is shown to imply the uniqueness of the usual propagator for a spin-zero particle of discrete mass.The classical definition of causality is then replaced by one appropriate for quantum theory. An additional type of equation is possible, which represents a particle with a continuous distribution of mass.