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But the diseases of the finite N theory do not arise here. In the limit, iN is kept fixed whereas instantons carry an action proportional to vi, without any further N-dependence. Consequently, bothersome instanton singularities will disappear from the Borel sum. In terms of iN, the theory is still only logarithmically asymptotically free, but on the other hand the expansion in terms of g 2N is much better behaved. The total number of different planar diagrams with L loops and E external lines is of order CL , where e depends on details of the theory [12].

Soon afterwards, in 1904, this was explicitly proved by G. Hamel [2]. Little by little under the influence of Klein and of his school it began to be recognized that invariance under the group of the automorphisms of space-time was the true criterion of objectivity for the physical laws. Already in 1910 Klein [3] explicitly stated that relativity was synonymous with invariance under a group and Klein's school systematically investigated the physical consequences of invariance under both finite and infinite dimensional Lie groups [4].

J. Wesfreid, Y. Pomeau, M. Dubois, C. Normand, P. Berge, Critical Effects in Rayleigh-Benard convection, J. , 7 (1978) 725. [16]. F. Busse, The Stability of finite amplitude cellular convection and its relation to an extremum principle, J. , 30 (1967) 625. [17]. D. H. Sattinger, Bifurcations and Symmetry Breaking in Applied Mathematics, Bull. Math. Soc. 3 (1980) 779. [18]. P. Curie, Sur la Symetrie dans les phenomenes physiques. Symetrie d'un champ electrique et d'un champ magnetique, Journal de Physique 3me Serie, 3 (1894) 393.

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