chapter  11
6 Pages

Digression: Violation Of Isotopic Spin

In this chapter we consider the currents associated with the chiral symmetry SU(3)L⊗SU(3)R, generated by chiral transformations of the triplet of light quarks u, d and s.

In place of the chiral currents, we can use the vector and axial vector currents which, in the quark model, are written:

V i = q¯ λi 2 γµq; (11.1)

Ai = q¯ λi 2 γµγ5q. (11.2)

In the limit of exact symmetry, the currents satisfy the continuity equations:

∂µJAµ = 0, (Jµ = Vµ, Aµ) (11.3)

and the charges:

QA =

∫ JA0 (x, t)d

3x3;

[QA, QB] = ifABCQC

are conserved.