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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. Gauge theories are also important in explaining gravitation in the theory of general relativity.
In theoretical physics, a non-abelian gauge transformation [1] means a gauge transformation taking values in some group G, the elements of which do not obey the commutative law when they are multiplied. By contrast, the original choice of gauge group in the physics of electromagnetism had been U(1), which is commutative.
BRST quantization is a differential geometric approach to performing consistent, anomaly-free perturbative calculations in a non-abelian gauge theory. The analytical form of the BRST "transformation" and its relevance to renormalization and anomaly cancellation were described by Carlo Maria Becchi, Alain Rouet, and Raymond Stora in a series of papers culminating in the 1976 "Renormalization of ...
Consider a generic (possibly non-Abelian) gauge transformation acting on a component field = =.The main examples in field theory have a compact gauge group and we write the symmetry operator as () = where () is an element of the Lie algebra associated with the Lie group of symmetry transformations, and can be expressed in terms of the hermitian generators of the Lie algebra (i.e. up to a ...
In any non-abelian gauge theory, any maximal abelian gauge is an incomplete gauge which fixes the gauge freedom outside of the maximal abelian subgroup. Examples are Examples are For SU(2) gauge theory in D dimensions, the maximal abelian subgroup is a U(1) subgroup.
This is a complication of the strong force making it inherently non-linear, contrary to the linear theory of the electromagnetic force. QCD is a non-abelian gauge theory. The word non-abelian in group-theoretical language means that the group operation is not commutative, making the corresponding Lie algebra non-trivial.
For non-abelian gauge groups that have a () subgroup, this mechanism agrees with the Higgs mechanism, but for other gauge groups there can appear discrepancies between the two approaches. Elitzur's theorem can also be generalized to a larger notion of local symmetries where in a D-dimensional space, there can be symmetries that act uniformly on ...
Non-abelian or nonabelian may refer to: Non-abelian group , in mathematics, a group that is not abelian (commutative) Non-abelian gauge theory , in physics, a gauge group that is non-abelian