  The question how to Lorentz transform an N-particle wave function naturally
leads to the concept of a so-called multi-time wave function, i.e. a map from
(space-time)^N to a spin space. This concept was originally proposed by Dirac
as the basis of relativistic quantum mechanics. In such a view, interaction
potentials are mathematically inconsistent. This fact motivates the search for
new mechanisms for relativistic interactions. In this paper, we explore the
idea that relativistic interaction can be described by boundary conditions on
the set of coincidence points of two particles in space-time. This extends
ideas from zero-range physics to a relativistic setting. We illustrate the idea
at the simplest model which still possesses essential physical properties like
Lorentz invariance and a positive definite density: two-time equations for
mass-less Dirac particles in 1+1 dimensions. In order to deal with a
spatio-temporally non-trivial domain, a necessity in the multi-time picture, we
develop a new method to prove existence and uniqueness of classical solutions:
a generalized version of the method of characteristics. Both mathematical and
physical considerations are combined to precisely formulate and answer the
questions of probability conservation, Lorentz invariance, interaction and
antisymmetry.
