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Families of Dirac operators with applications to physics. (English) Zbl 0603.58054
Élie Cartan et les mathématiques d’aujourd’hui, The mathematical heritage of Elie Cartan, Semin. Lyon 1984, Astérisque, No.Hors Sér. 1985, 323-340 (1985).
[For the entire collection see Zbl 0573.00010.]
From the introduction: ”Currently, the set of connections on a principal bundle (vector potentials or Yang-Mills fields) is a fruitful unifying principle in physics. The quantization of such fields, particularly when the group of the bundle is non-abelian, presents serious difficulties and is not well understood. Some aspects of these problems, however, do lend themselves to a mathematical treatment, and in this talk the author attempts to give an exposition, for mathematicians, of one such topic – chiral anomaly.”
Reviewer: N.Jacob

58J90 Applications of PDEs on manifolds
58J10 Differential complexes
81T08 Constructive quantum field theory