His topics include symmetries and conservation laws, tensors and tensor operations, special relativity and the physical particle states, spontaneous symmetry breaking and the unification of the electromagnetic and weak forces, the Goldstone theorem and the consequent emergence of nonlinearity transforming massless Goldstone bosons
, the simple sphere, and beyond the standard model.
Here, [[phi].sub.k] denotes the octet of would-be Goldstone bosons ([pi], K, [[eta].sub.8]) arising out of spontaneous breaking of chiral SU[(3).sub.L] [cross product] SU[(3).sub.R] symmetry, [[eta].sub.0] is the singlet boson, and Q is the topological charge density; [chi] = diag[[m.sup.2.sub.[pi]], [m.sup.2.sub.[pi]], (2[m.sup.2.sub.k] - [m.sup.2.sub.[pi]])] is the meson mass matrix, the pion decay constant [F.sub.[pi]] = 92.4 MeV, and [F.sub.0] renormalizes the flavor-singlet decay constant.
Heavy baryon chiral perturbation theory is the effective field theory of the standard model at low energies in the baryonic sector which can be successfully applied with Goldstone bosons included.
Additionally, an important consequence of the axial anomaly is the fact that the would-be Goldstone boson, [eta]', is massive even in the chiral limit .
It has a justification in 1/[N.sub.C] expansion of QCD [2-4], where the axial anomaly is suppressed by powers of 1/[N.sub.C] and [eta]' appears as a ninth Goldstone boson. Since there is no anomaly in the leading order of the 1/[N.sub.C] expansion, it is natural to expect that, up to leading order, the singlet NG boson is present and degenerate with other ([N.sup.2.sub.f] - 1) nonsinglet NG bosons in the chiral limit.
Observables can then be expanded simultaneously in the Goldstone boson octet masses and the [eta]' mass that does not vanish in the chiral limit.