Reduction of scattering to an invariant finite displacement in an ambient space-time
AUTOR(ES)
Segal, I. E.
RESUMO
The scattering transformation S for a wave equation in Minkowski space M0 is reducible (rigorously in the classical case, necessarily partially heuristically in the nonlinear quantum case) to the action of a distinguished finite transformation ζ in the ambient universal cosmos M. M0 is invariantly imbedded in M, relative to any given point of observation, and the space-like surfaces x0 = s in M0 converge as s → ±∞ to finite light cones C± in M. The generator ζ of the infinite cyclic center of the connected group of all casuality-preserving transformations in M (isomorphic to SU(2,2)/Z2) 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.
