Gauge invariance in quantum electrodynamics

Abstract

The object of this dissertation is to present a survey of papers written on gauge invariance in the past decade. Up till 1955 mainly c-number gauges were used. The generalisation to q-number gauges, however, has introduced many simplifications, especially in calculations involving infrared and ultraviolet divergences. These calculations (cf. the Lamb Shift) are too long to be given here, and we limit ourselves to a discussion of the various types of propagators used in them.

Invariance under gauge transformations is rather different from invariance under Lorentz transformations. The invariance of a Lagrangian under translations and rotations is a physical requirement, while the invariance under some type of gauge transformation is determined by the existence of a physical conservation law.

Chapters I and II are really introductory, dealing only with the properties of free and Interacting fields. The renormalization programme is given in detail in Chapter III, and In the final two chapters the gauge properties of propagators and renormalization constants are examined.