Gauge fields and flavor oscillations

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. 2.1 ), 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 in Stueckelberg’s original diagram, in the presence of a nonabelian gauge field, can induce a flavor change on the particle line, resulting in a transition to an antiparticle with different identity. An even number of such transitions can result in flavor oscillations, such as in the simple case of neutrino oscillations. On the quark constituent level, such transitions can be associated with K, B or D meson oscillations as well. The construction of the Lorentz force acting on particles with abelian or nonabelian gauge will also be discussed, with results consistent with the assumptions for the semiclassical model. In view of our discussion of the previous chapter, it will also be shown that this picture could provide a fundamental mechanism for CP violation.