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It remains to say a word about strong interactions, which we also want to incorporate into the gauge picture. I can be very brief, because this subject is fully developed in the lectures of H. Fritzsch. Let me just mention, that it is the colour symmetry which is gauged to lead to a gauge theory of strong interactions. Thus, we are indeed on our way to unify the interactions of elementary particles which is one of the longstanding dreams of physicists. I am indebted to Dr. G. Ecker for a critical reading of the manuscript.
12 (1964) 132; Phys. Rev. Lett. 13 (1964) 508; Phys. Rev. 145 (1966) 1156. 3. 4. 5. 6. 7. 8. B. Kibble, Phys. Rev. W. Anderson, Phys. Rev. 130 (1963) 439; for a review cf. J. Bernstein, Rev. Mod. Phys. 46 (1974) 7. S. W. Lee, Gauge Theories (Physics Reports 9C/1, Nov. 1973). C. Tay1or, Gauge Theories of Weak Interactions (Cambridge Univ. Press, 1976). C. Bouchiat, J. I1iopou1os and Ph. Meyer, Phys. Lett. 38B (1972) 519. G. t'Hooft, Nuc1. Phys. B35 (1971) 167. L. Adler, Phys. Rev. 177 (1969) 2426.
9) c we can write eq. 10) c or -+ W' lJ -+ -+ + Cl lJ lJ - w W -+ -+ g [w x W ] lJ The analogy to eq. 7) is now much more obvious. 11). do have the extra term in eq. Just as in section 2 our next problem is to find the "free Lagrangian" for the gauge fields. Let us first try an ansatz identical to eq. -+ F lJ\! Cl -+ lJ W \! 8), Le. 12) W \! lJ -+ -+lJ\! 11), we find that FlJ\! F is not gauge invariant. Rather we get But by using eq. -+ -+ lJ\! F ' F ' lJ\! = -+ -+lJ\! -+lJ\! F lJ\! F + 4g F ~ 0 -+ \!