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Euclidean Quantum Field Theory. I: Equations for a Scalar Model... - Couverture souple

Symanzik, Symanzik

 
9781314919950: Euclidean Quantum Field Theory. I: Equations for a Scalar Model...

Synopsis

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Présentation de l'éditeur

Abstract The analytic continuations to imaginary time of the Green sfunctions of local quantum field theory define Euclidean Green sfunctions. Use of the proper-time method allows to represent these functions as multiple Wiener integrals of functionals that obey an infinite system of coupled integral equations which are similar to, and for the particular model of a complex scalar field in quadrilinear self-interaction considered here a limiting case of, systems studied in quantum statistical mechanics by Ginibre. As a consequence, theE uclidean Green sfunctions can for this model be obtained by a limiting process, with temperature and density going to infinity, from the reduced density matrices of a nonrelativistic Bose gas. Reduced functionals are defined and their equations determined as a preparatory step to renormalization in the superrenormalizable cases of two and three dimensions.
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