Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-10-18
Physics
High Energy Physics
High Energy Physics - Theory
32 pages, LaTeX, MS-TPI-94-12, Talk presented at the conference ``Constructive Results in Field Theory, Statistical Mechanics
Scientific paper
10.1007/3-540-59190-7_22
In this talk methods for a rigorous control of the renormalization group (RG) flow of field theories are discussed. The RG equations involve the flow of an infinite number of local partition functions. By the method of exact beta-function the RG equations are reduced to flow equations of a finite number of coupling constants. Generating functions of Greens functions are expressed by polymer activities. Polymer activities are useful for solving the large volume and large field problem in field theory. The RG flow of the polymer activities is studied by the introduction of polymer algebras. The definition of products and recursive functions replaces cluster expansion techniques. Norms of these products and recursive functions are basic tools and simplify a RG analysis for field theories. The methods will be discussed at examples of the $\Phi^4$-model, the $O(N)$ $\sigma$-model and hierarchical scalar field theory (infrared fixed points).
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