Free field theories of spin-mass trajectories and quantum electrodynamics in the null plane

Abstract

The ten generators of the Poincar\'e algebra for quantum electrodynamics and other gauge field theories are given in the null plane such that they all explicitly correspond, in the free-field case, to the Bacry-Chang group-theoretic forms. The internal oscillator content is extracted for both gauge theories and dual resonance models. In contrast to manifestly covariant or other theories, Bacry-Chang-type generators have the advantages of not referring to dependent spin components and of being rational in the canonical variables. The last property implies a simple position-space representation. Since the forms are independent of spin magnitude and allow inclusion of charge quantum numbers at will, they seem to represent an advantageous free-particle starting point for a hadron field theory with positive spin-mass trajectories (SMT) and with interaction. The interaction terms from manifestly covariant theories are considered in the null plane and found to be cubic and quartic in the fields. A straightforward extension of these interactions to SMT has not been found. The dual model, however, encompasses SMT and is known to have interactions even though the full details of the model's interaction terms are not worked out here. Consequently, the approach indicates how a realistic spectrum might be achieved without composite hadrons and incorporating full Poincar\'e invariance.