Massachusetts Institute of Technology, Cambridge, MA 02139.
Proc Natl Acad Sci U S A. 1984 Nov;81(22):7266-8. doi: 10.1073/pnas.81.22.7266.
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.
在闵可夫斯基空间 M(0)中的波动方程的散射变换 S 可（在经典情况下严格地，在非线性量子情况下必要地部分启发式地）简化为环境普遍宇宙 M 中一个特殊的有限变换 zeta 的作用。M(0)相对于任何给定的观察点在 M 中是不变嵌入的，并且时空间隔 x(0) = s 在 M(0)中随着 s --> +/-无穷大收敛到 M 中的有限光锥 C(+/-)。在 M 中所有保持因果关系的变换的连通群的无限循环中心的生成元 zeta（同构于 SU(2,2)/Z(2)）将 C(-)带入 C(+)，并在不变束的表述中作为 S 作用于相对论波动方程的解上。S 的建立得到简化，S 的对称性和正则性得到增强，散射概念的范围扩展到重要的方程，如缺少不变的自由和相互作用分量的杨-米尔斯方程，并且束缚态和散射态的处理更加统一。
