Abstract
We introduce the concept of equivalence among Wilson actions. Applying the concept to a real scalar theory on a euclidean space, we derive the exact renormalization group transformation of K. G. Wilson, and give a simple proof of universality of the critical exponents at any fixed point of the exact renormalization group transformation. We also show how to reduce the original formalism of Wilson to the simplified formalism by J. Polchinski.
Highlights
The purpose of this paper is to introduce the concept of equivalence among Wilson actions
VI, we assume a fixed point of the exact renormalization group (ERG) transformation, and show that the critical exponents defined at the fixed point are independent of the choice of cutoff functions
II to show the universality of critical exponents at a fixed point of the ERG transformation, by which we mean the independence of critical exponents on the choice of cutoff functions K, k
Summary
The purpose of this paper is to introduce the concept of equivalence among Wilson actions. If two Wilson actions describe the same low energy physics, we regard them as equivalent It is the purpose of this paper to provide a concrete definition of equivalence using the continuum approach. III we derive the exact renormalization group (ERG) transformation of Wilson [1] by considering a particular type of equivalence. VI, we assume a fixed point of the ERG transformation, and show that the critical exponents defined at the fixed point are independent of the choice of cutoff functions. This is what we mean by universality.
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