Bulg. J. Phys. vol.33 no.s3 (2006), pp. 080-90



The Role of Conformal Field Theory in Mathematical Physics

I.T. Todorov
Institute for Nuclear Research and Nuclear Energy, 72 Tsarigradsko Chaussee Blvd., BG-1784 Sofia, Bulgaria
Abstract. Conformal field theory (CFT) provides an early example of what is now termed ``Physical Mathematics'': the 1936 Dirac's paper on wave equations in conformal space is motivated by mathematical beauty rather than by physical necessity.
The talk surveys some memorable developments of the past fifty years including results of a joint effort by German and Bulgarian theorists. We conclude by reviewing the recently proposed notion of global conformal invariance in Minkowski space which allows us to extend ideas of 2-dimensional CFT and vertex algebras to higher dimensions.

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