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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 transformations (called * gauge transformations * ) must form a [Lie group] which is referred to as the * symmetry group * or the * gauge group * of the theory. Associated with any Lie group is the [Lie algebra] of [group generator] s. 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 (called * gauge invariance * ). When such a theory is quantized, the [quanta] of the gauge fields are called [gauge boson] * s * . If the symmetry group is [non-commutative] , the gauge theory is referred to as * non-abelian * , the most usual example of which being the [Yang–Mills theory] .

Gauge theories are important as the successful field theories explaining the dynamics of [elementary particles] . [Quantum electrodynamics] is an [abelian] gauge theory with the symmetry group [U(1)] and has one gauge field, the [electromagnetic field] , with the [photon] being the gauge boson. The [Standard Model] is a non-abelian gauge theory with the symmetry group [U(1)] × [SU(2)] × [SU(3)] and has a total of twelve gauge bosons: the [photon] , three [weak boson] s and eight [gluons] .

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