Non-Usual Topologies on Space-Time and High Energy Scattering

Motivated by recently observed deviations from quantum electrodynamical theory, we study the possibility that our notions of space‐time may need revision at small distances. In this work, we wish to call attention to certain techniques which are available for studying different space‐time structures within the framework of topology. Our main effort is in the consideration of a non‐usual topology on space‐time in which is embedded an elementary length. By working separately in each n‐particle subspace, the embedding is done in an inhomogeneous Lorentz invariant way, and we avoid any lattice structure in space‐time. Particles in this topology are in general extended structures, and we find the surprising feature that, at high energies, the topology enhances backward and large‐angle scattering. From these preliminary investigations, we are not as yet able to make more than qualitative comparison with experiment. Along the way, we have the opportunity to remark on ways of embedding an intrinsic breakdown of certain invariances (e.g., parity) in the topology of space‐time.