Quantum Field Theories in the Infinite-Momentum Frame. IV. Scattering Matrix of Vector and Dirac Fields and Perturbation Theory

Abstract

The scattering matrix of coupled spin-one and Dirac field theories formulated in light-front quantization of the preceding paper is studied. The scattering matrix of the vector-gluon model in this new formulation is shown to give the same predictions as in the equal-time formulation to all orders in perturbation theory. Renormalizability of this model in the new formulation is also established. A further test of the light-front quantization of spin-one fields is discussed by examples of fermion-fermion interaction and virtual as well as real Compton scattering in the axial-vector-gluon model in the lowest-order perturbation theory. A reduction formula for vector particles is derived and the Wick theorem is proved. Peculiarities in the perturbation theory of the light-front formulation are discussed. Finally, a partonlike model for scattering of two energetic particles is proposed which satisfies manifest $s$-channel unitarity.