chapter  3
10 Pages

YANG–MILLS THEORY

Electrodynamics is invariant under so-called gauge transformations of the second type:

ψ(x)→ ψ′(x) = eiqφ(x)ψ(x); Aµ(x)→ A′µ(x) = Aµ(x) − ∂µφ(x) (3.1) where φ is an arbitrary function of space-time, ψ is a generic matter field, q is its electric charge in units of the elementary charge (for the electron field, q = −1) and Aµ is proportional to the electromagnetic field.