Chapter 28: Gauge Transformation

Gauge theories study invariance of a field theory with Lagrange function or Lagrange density under internal global symmetry transformations of a Lie symmetry group G which are extended to transformations which are extended to transformations which can be different at different space-time points. So global Lie symmetry groups are independent of the space time point. Local or gauge transformations depend on (x₀, x₁, x₂, x₃) (x₀ = ct). If a set of physical laws is invariant under a global Lie symmetry transformation, the requirement of invariance under gauge Lie symmetries demands the introduction of new fields, the so-called gauge fields. The simplest case is the Lie group U(1). In most cases the starting point is the Lagrange function or Lagrange density…