| Scaling And Functional Integration And Brydges' Operator In Renormalization Theory (2007) | |||||||||||||||
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| In previous papers, we introduced an axiomatic scheme for the functional integrals used in quantum mechanics. Here we extend this scheme to quantum eld theory. Using a method recently introduced by Brydges, Hurd and Dimock, we consider a functional partial differential equation of parabolic type which governs the renormalization group transformations. Unlike our predecessors, we deal directly with the theory in the Minkowski space, without resorting to the Euclidean version and analytic continuation of Schwinger functions. In physical terms, the scaling parameter is treated like an additional dimension for space-time. 1 Scaling and Functional Integration Pierre Cartier Ecole Normale Superieure, 45 rue d'Ulm, F-75230 Paris Cedex 05, France Cecile DeWitt-Morette Center for Relativity and Department of Physics, The University of Texas at Austin, Austin, Texas 78712-1081 Introduction Path integration is by now a well-designed tool [1] reliable and powerful for systems with a nite ... | |||||||||||||||
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