Commutators on Characteristic Surfaces

The Lagrangian formalism is employed to derive the commutation relations on null surfaces for relativistic field theories. The theories treated are the Klein-Gordon field, the Maxwell field, the linearized gravitation theory, and the general theory of relativity. Special attention is paid to the treatment of null surfaces at infinity, on which we are able to obtain the commutation relations for the "news function," which represents the independent radiation modes of the field. For the general theory of relativity, the methods of this paper seem appropriate only when we truncate the theory by excluding solutions which are not asymptotically flat in the sense of Penrose.