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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.
In the summer 1953, Yang and Mills extended the concept of gauge theory for abelian groups, e.g. quantum electrodynamics, to non-abelian groups, selecting the group SU(2) to provide an explanation for isospin conservation in collisions involving the strong interactions. Yang's presentation of the work at Princeton in February 1954 was ...
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.
In an abelian (commutative) group (such as the U(1) we use here) the structure constants vanish, since the generators t a all commute with each other. Of course, this is not the case in general – the standard model includes the non-Abelian SU(2) and SU(3) groups (such groups lead to what is called a Yang–Mills gauge theory).
A gauge theory is a type of theory in physics. The word gauge means a measurement , a thickness, an in-between distance (as in railroad tracks ), or a resulting number of units per certain parameter (a number of loops in an inch of fabric or a number of lead balls in a pound of ammunition ). [ 1 ]
QCD is a non-abelian gauge theory (or Yang–Mills theory) of the SU(3) gauge group obtained by taking the color charge to define a local symmetry. Since the strong interaction does not discriminate between different flavors of quark, QCD has approximate flavor symmetry, which is broken by the differing masses of the quarks.
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 ...