Discrete Symmetries for the Bound State Problem of Positronium in Light-Cone Quantization

I use as the starting point the effective kernel for positronium which Alex Langnau and I constructed to impliment discrete symmetries. It is found that implimenting charge conjugation makes obvious rotational and gauge symmetry violation in the Hamiltonian which can be fixed by adding counterterms to the Hamiltonian. This induces charge symmetry violation as well as rotational symmetry violation in the electromagnetic current matrix elements. Gauge symmetry is found to be maintained . ? Work supported by the Department of Energy, contract DE-AC03-76SF00515 1. Introduction In this paper I continue the study of positronium which Alex Langnau and I started, 1 which presented a novel solution to the equation Hj\Psi ?= M 2 j\Psi ? (1:1)1 Here H is P \Gamma , the Hamiltonian of the system, and \Psi is a superposition of infinite number of all the possible Fock states. Discrete symmetry of charge conjugation is implimented so as to compute the singletriplet mass splitting. It is foun..