Gluons carry color charges and hence interact with each other even in the absence of quarks. The non-Abelian gauge field in QCD mediates color interactions between quarks. In 1970s the idea of the extra quantum number, color, for quarks was established and the theory of quark dynamics was found to be a non-Abelian gauge theory with SU(3) symmetry that was named quantum chromodynamics (QCD). These facts strongly support the idea that quarks should have an extra quantum number, color. ![]() (5) is much smaller than experimental data. ![]() If there is no color degree of freedom, the prediction of Eq. (5) with the data strongly support N c = 3. Where s is the center-of-mass total energy squared of the e + e − system, Q i is the charge of the ith quark, and N f is the number of flavors of quarks which may contribute to the process. (5) σ ( e + e − → hadrons ) = 4 π α 2 3 s N c ∑ i = 1 N f Q i 2 , It contains one spinor conjugacy class in addition to the adjoint conjugacy class. It turns out that the particular Lie group that is appropriate is Spin (32)/ Z 2. There are several different Lie groups that have the same Lie algebra. The term SO (32) is used here somewhat imprecisely. For any other choice there are fatal anomalies. Now we see that at the quantum level, the only choice that is consistent is SO (32). (This result was obtained by Green and Schwarz, 1984a.)Īs we mentioned earlier, at the classical level one can define type I superstring theory for any orthogonal or symplectic gauge group. For these two choices, all the anomalies cancel. This theory has both gauge and gravitational anomalies for every choice of Yang–Mills gauge group except SO (32) and E 8 × E 8. Type I supergravity coupled to super Yang–Mills. (This result was obtained by Alvarez–Gaumé and Witten, 1983.) However, when their contributions are combined, the anomalies all cancel. This theory has three chiral fields each of which contributes to several kinds of gravitational anomalies. This theory is nonchiral, and therefore it is trivially anomaly-free. ![]() This theory has anomalies for every choice of gauge group. There are several possible cases in ten dimensions: The anomalies can be attributed to the massless fields, and therefore they can be analyzed in the low-energy effective field theory. The method is illustrated for scattering processes in the oceanic wave guide involving surface and internal gravity waves, horizontal currents (turbulence), seismic waves, and bottom irregularities.In the case of ten-dimensional chiral gauge theories, the potentially anomalous Feynman diagrams are hexagons, with six external gauge fields. This is offset by simpler interaction rules and a closer correspondence between the perturbation graphs and collision diagrams. It has the unrealistic property that the energies and number densities of antiparticles are negative. The representation follows closely the standard treatment of nonlinear lattice vibrations, but the particle picture differs from the usual phonon interpretation of lattice waves. The derivation of the transfer expressions can then be reduced to a few general rules for the construction of the diagrams and the associated collision cross sections. In the particle picture, the interactions can be conveniently described by Feynman diagrams, which may be regarded either as branch diagrams of the perturbation expansion or as collision diagrams. The energy transfer due to weak nonlinear interactions in random wave fields is reinterpreted in terms of a hypothetical ensemble of interacting particles, antiparticles, and virtual particles.
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