Reduction of scattering to an invariant finite displacement in an ambient space-time.
The scattering transformation S for a wave equation in Minkowski space M(0) is reducible (rigorously in the classical case, necessarily partially heuristically in the nonlinear quantum case) to the action of a distinguished finite transformation zeta in the ambient universal cosmos M. M(0) is invariantly imbedded in M, relative to any given point of observation, and the space-like surfaces x(0) = s in M(0) converge as s --> +/-infinity to finite light cones C(+/-) in M. The generator zeta of the infinite cyclic center of the connected group of all casuality-preserving transformations in M (isomorphic to SU(2,2)/Z(2)) carries C(-) into C(+) and acts on solutions of relativistic wave equations as S, in an invariant bundle formulation. The establishment of S is simplified, the symmetry and regularity properties of S are enhanced, the scope of the scattering concept is extended to important equations such as those of Yang-Mills (lacking an invariant separation into free and interaction components), and the treatment of bound and scattering states is more unified.
Segal
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Massachusetts Institute of Technology, Cambridge, MA 02139.