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Fate of classical symmetry in field theory: An analysis of quark mass generation through the dilatation anomaly by a nonlinear chiral transformation. (English) Zbl 0845.53052

Gruber, Bruno (ed.), Symmetries in science VI: From the rotation group to quantum algebras. Proceedings of a symposium held in Bregenz, Austria, August 2-7, 1992. New York, NY: Plenum Press. 359-366 (1993).
This is a paper based on a dedicatory talk given on the occasion of a felicitation to Prof. Biedenharn, an intellectual giant and great doyen of theoretical physics of the recent years. It deals with the role of anomaly in classical symmetry breaking. The anomaly in the path integral is discussed. The W-T identity from a nonlocal nonlinear transformation is dealt with. The case of QCD is also briefly touched upon. Under the title “Fate of the symmetry in field theory”, the questions of quark mass generation, the dilatation anomaly and the possible new domain of problems arising are discussed.
For the entire collection see [Zbl 0835.00011].

MSC:

53Z05 Applications of differential geometry to physics
81R40 Symmetry breaking in quantum theory
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