  In relativistic quantum mechanics wave functions of particles satisfy field
equations that have initial data on a space--like hypersurface. We propose a
dual field theory of ``wavicles'' that have their initial data on a time--like
worldline. Propagation of such fields is superluminal, even though the Hilbert
space of the solutions carries a unitary representation of the Poincare group
of mass zero. We call the objects described by these field equations
``Kairons''. The paper builds the field equations in a general relativistic
framework, allowing for a torsion. Kairon fields are section of a vector bundle
over space-time. The bundle has infinite--dimensional fibres.
