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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 ...
In theoretical physics, scalar electrodynamics is a theory of a U(1) gauge field coupled to a charged spin 0 scalar field that takes the place of the Dirac fermions in "ordinary" quantum electrodynamics. The scalar field is charged, and with an appropriate potential, it has the capacity to break the gauge symmetry via the Abelian Higgs mechanism.
The Stueckelberg extension of the Standard Model (StSM) consists of a gauge invariant kinetic term for a massive U(1) gauge field.Such a term can be implemented into the Lagrangian of the Standard Model without destroying the renormalizability of the theory and further provides a mechanism for mass generation that is distinct from the Higgs mechanism in the context of Abelian gauge theories.
For the leptons, the gauge group can be written SU(2) l × U(1) L × U(1) R. The two U(1) factors can be combined into U(1) Y × U(1) l, where l is the lepton number. Gauging of the lepton number is ruled out by experiment, leaving only the possible gauge group SU(2) L × U(1) Y. A similar argument in the quark sector also gives the same result ...
B μ is the U(1) gauge field, Y W is the weak hypercharge – the generator of the U(1) group, W → μ is the 3-component SU(2) gauge field, L are the Pauli matrices – infinitesimal generators of the SU(2) group – with subscript L to indicate that they only act on left-chiral fermions, g' and g are the U(1) and SU(2) coupling constants ...
Such a U(1) group is non-compact. The field θ transforms as an affine representation of the gauge group. Among the allowed gauge groups, only non-compact U(1) admits affine representations, and the U(1) of electromagnetism is experimentally known to be compact, since charge quantization holds to extremely high accuracy.
Mathematically, electromagnetism is unified with the weak interactions as a Yang–Mills field with an SU(2) × U(1) gauge group, which describes the formal operations that can be applied to the electroweak gauge fields without changing the dynamics of the system.
In particle physics, a gauge boson is a bosonic elementary particle that acts as the force carrier for elementary fermions. [1] [2] Elementary particles whose interactions are described by a gauge theory interact with each other by the exchange of gauge bosons, usually as virtual particles. Photons, W and Z bosons, and gluons are gauge