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By Professor Dr. J. Wess (auth.)

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Extra resources for Springer Tracts in Modern Physics, Volume 60

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G o l d s t o n e To this point we have discussed only vaguely the idea of an approximate chiral S U(2) | S U(2) (or S U(3) | S U(3)) symmetry for the strong interactions. I have also hinted that we would find that this had to be an approximate symmetry of a rather unusual kind. What I would like to do in this lecture is discuss in some detail just what is unusual about this 'symmetry' and provide you with enough background material to make you somewhat comfortable with these ideas. Before entering into this discussion however, let me briefly summarize what the results of our discussion will be.

4"(x) + [f~/(1 + f2)] ~o2{(q~x duq~)9V" -f~q~uq~. 18) n and letting ~(x)= ~ ~ie +i~*'x keeping only those terms in which each i=l of the qi's appears exactly once. (As in previous cases, the bar above the axial-vector current indicates that its single-meson poles in any one of the q2,s have been removed). Note that crossing symmetry allows us to get any other meson amplitude by merely changing the sign of the q,'s, which in effect gives us the amplitude for the ith _ pion inserted in state [B).

Stands for Schwinger terms; (all time ordered products will be assumed to be defined to be covariant so that Schwinger terms can be ignored). t. T. where J2 stands for some definite current. T. g. t. : We are classifying currents by their third component of isospin and their hypercharge. Thus A,~+ = A x + iA2, A,~o = A3, A1r = A4+,A5 etc. If we accept (as we shall) the usual current-current picture for the leptonic and semi-leptonic weak interactions the constants (2f~) -~ (0~= 1.... 2) (where [M,(q)) stands for a pseudoscalar meson of momentum q) are experimentally determined by studying the decays M ~ lepton + neutrino.

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