Abstract
We discuss a general method of constructing the products of composite operators using the exact renormalization group formalism. Considering mainly the Wilson action at a generic fixed point of the renormalization group, we give an argument for the validity of short distance expansions of operator products. We show how to compute the expansion coefficients by solving differential equations, and test our method with some simple examples.
Highlights
In the framework of the Wilsonian renormalization group (RG), the physics of a system is completely characterized by a Wilson action
The momentum cutoff of the action is fixed by rescaling while the corresponding size in physical units diminishes exponentially under the RG transformation
It is important to understand how small deformations of the fixed-point Wilson action grow under the RG transformation
Summary
In the framework of the Wilsonian renormalization group (RG), the physics of a system is completely characterized by a Wilson action. Particular attention is paid to the ERG differential equation satisfied by composite operators and their products at the fixed point. [24] that the high-momentum limit of W and gives the corresponding functionals without the infrared cutoff.) The ERG equations satisfied by W and are given Let O(p) be a composite operator of scale dimension −y and momentum p Regarding it as a functional of J , we obtain the following ERG equation: D+2 δ y + p · ∂p O(p) =. In the absence of mixing the last counterterm satisfies yi + p · ∂p + · · · + s · ∂s − D P1234 (p, q, r, s) This can be generalized to higher-order products of composite operators.
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