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Reference19 articles.
1. Most of the relevant concepts can be found inK. G. Wilson:Phys. Rev.,179, 1499 (1969);H. Fritzsch andM. Gell-Mann:Proceedings of the International Conference on Duality and Symmetry in Hadron Physics, edited byE. Gotsman (Jerusalem, 1971).
2. For the definition of contraction of Lie groups see, for instance,R. Hermann:Lie Groups for Physicists (New York, N. Y., 1966), p. 86.
3. C. G. Callan, S. Coleman andR. Jackiw:Ann. of Phys.,59, 42 (1970).
4. It is well known that the integral appearing on the right-hand side of eq. (1.1b) does not converge in any sense to a well-defined operator if the theory is represented in a Hilbert space possessing a vacuum state. This does not however give rise to difficulties in the following since we shall only deal with commutators ofD(Dx 0) and local operators which can be defined correctly.
5. A more general situation could be envisaged in which some of the fieldsψ i belong to «dilatation multiplets» (G. Dell’Antonio: New York University report 12/72 (1972)). For simplicity we are assuming here that the fieldsψ i belong to one-dimensional representations of the dilatation. The extension to the more general situation is straightforward. For a general treatment of the commutators among conformal generators in the presence of breaking, seeR. Gatto andG. Sartori:Nuovo Cimento,7 A, 99 (1972).
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