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 four-potential , 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 bosons and eight gluons .
In mathematics , the unitary group of degree n , denoted U( n ), is the group of n × n unitary matrices , with the group operation of matrix multiplication . The unitary group is a subgroup of the general linear group GL( n , C ) . Hyperorthogonal group is an archaic name for the unitary group, especially over finite fields.