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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 ...
In gauge theory, especially in non-abelian gauge theories, global problems at gauge fixing are often encountered. Gauge fixing means choosing a representative from each gauge orbit, that is, choosing a section of a fiber bundle. The space of representatives is a submanifold (of the bundle as a whole) and represents the gauge fixing condition.
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.
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 ...
Pages in category "Gauge theories" The following 82 pages are in this category, out of 82 total. ... Non-abelian gauge transformation; P. Path-ordering;
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 ...