Gauge theory
In physics, a
gauge theory is a type of field theory in which the Lagrangian is invariant under a continuous group of local transformations. The term
gauge refers to redundant degrees of freedom in the Lagrangian. The transformations between possible gauges, called
gauge transformations, form a Lie group—referred to as the
symmetry group or the
gauge group of the theory. Associated with any Lie group is the Lie algebra of group generators. For each group generator there necessarily arises a corresponding vector field called the
gauge field. Gauge fields are included in the Lagrangian to ensure its invariance under the local group transformations. When such a theory is quantized, the quanta of the gauge fields are called
gauge bosons. If the symmetry group is non-commutative, the gauge theory is referred to as
non-abelian, the usual example being the Yang–Mills theory. Many powerful theories in physics are described by Lagrangians that are invariant under some symmetry transformation groups.