SELF-DUAL MAXWELL FIELD ON A NULL CONE

An an introduction to the use of self-dual variables on a null cone, the Hamiltonian for the Maxwell field is set up on a null cone in Minkowski space. In this treatment, the vector potential (the connection) and the self-dual components of the Maxwell field are treated as independent configuration space variables. Because the initial surface is a null cone, additional primary and secondary constraints arise. These constraints can be grouped into first class and second class. The elimination of the second class constraints together with the reality conditions on the vector potential, reduce the independent phase space variables to two. In its final form the Hamiltonian can be expressed in terms of the product of the self-dual Maxwell field and its complex conjugate.