Problems and fashion in mathematical physics

Impressive parallel developments in pure mathematics and in quantum field theory has revived Felix Klein's vision of a "preestablished harmony between mathematics and physics" and encouraged the appearance of a new - we may call it "Pythagorean" - brand of mathematical physics. A telling example is provided by "the Fock space of positive integers" introduced by Bost and Connes [1]. Conformal field theory had an important part in bridging the gap between mathematics and quantum field theory [2]. I shall also cite some sharp criticisms of string theory (which pretends to offer the modern realization of the Pythagorean dream).

  1. J.B. Bost, A. Connes, Hecke algebras, type III factors and phase transition with spontaneous symmetry breaking in number theory, Selecta Math. (New Series) 1:3 (1995) 411-457.
  2. I.T. Todorov, Two-dimensional conformal field theory and beyond. Lessons from a continuing fashion, Lett. Math. Phys. 56 (2001) 151-161; Vienna preprint ESI 986 (2001).

Ivan Todorov

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