Chapter 7: Gauge Fields for Relativistic Mechanics

In this chapter we discuss the general formulation of gauge fields in the quantum theory, both abelian and nonabelian. A generalization of the elementary Stueckelberg diagram (Fig. 1 of Chapter 2), demonstrating a “classical” picture of pair annihilation and creation, provides a similar picture of a process involving two or more vertices (diagrams of this type appear in Feynman’s paper in 1949 [Feynman (1949)] with sharp instantaneous vertices). A single vertex, as it was in Stueckelberg’s original diagram, in the presence of a nonabelian gauge field, can induce a transition to an antiparticle with different identity. Such transitions can result in “flavor oscillations”, such as in the simple case of neutrino oscillations, transitions between electron and muon neutrinos. We shalll discuss this situation briefly here. The construction of the Lorentz force will also be discussed…