The Hamiltonian for the Einstein equations is constructed on a outgoing null cone with the help of the usual null tetrad. The resulting null surface constraints are shown to be second class in the terminology of Dirac. These second class constraints are eliminated by use of the “starring” procedure of Bergmann and Komar.

The canonical formalism for the Maxwell field on a null surface has been revisited. A new pair of gauge-independent canonical variables is introduced. It is shown that these variables are derivable from a Hamillon-Jacobi functional. The construction of the appropriate C * algebra is carried out in preparation for quantization. The resulting quantum theory is similar to a previous result. It is then shown that one can construct the T-variables of Rovelli and Smolin on the null surface. The Poisson bracket (...) algebra exhibits causal relations along the null rays, but is nonsingular if the loops are restricted to those whose projections along the null rays are not tangent and one-to-one. Finally, there is a brief discussion of the relevance of this work to general relativity. (shrink)