Self-dual Maxwell field on a null surface. II

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.It is a pleasure to dedicate this paper to Fritz Rohrlich who has been a collegue at Syracuse University for the past 30 years. We both came to Syracuse at the same time. Indeed, Fritz called me to induce me to do so at a time when I was still considering the move. I have never regretted following his lead.