Nonassociative Algebras and Nonperturbative Field Theory for Hierarchical Models

Details Nonassociative Algebras and Nonperturbative Field Theory for Hierarchical Models Nonassociative Algebras and Nonperturbative Field Theory for Hierarchical Models

1994-06-07

arxiv.org/abs/hep-lat/9406005v1

Physics

High Energy Physics

High Energy Physics - Lattice

74 pages, report MS-TPI-94-04

Scientific paper

Hierarchical renormalization group (RG) transformations are related to nonassociative algebras. These algebras serve as a new basic tool for a rigorous treatment of global RG flows and the search of nontrivial infrared fixed points. Convergent expansion methods are presented and analyzed in terms of algebra norms. It is shown that the infrared fixed points are solutions of a quadratic equation with an infinite number of unknowns. A continuous manifold of two dimensional periodic nontrivial fixed points is presented in terms of theta functions. Local Borel summability of the $\epsilon$- expansion for n-well fixed points is proved by algebraic methods.

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