A Scheme Independent Definition of ΛQCD\Lambda_{\rm QCD}

Given a renormalization scheme of QCD, one can define a mass scale $\Lambda_{\rm QCD}$ in terms of the beta function. Under a change of the renormalization scheme, however, $\Lambda_{\rm QCD}$ changes by a multiplicative constant. We introduce a scheme independent $\Lambda_{\rm QCD}$ using a connection on the space of the coupling constant.Comment: 4 pages, harvma

Bootstrapping Perturbative Perfect Actions

We study the exact renormalization group of the four dimensional phi4 theory perturbatively. We reformulate the differential renormalization group equations as integral equations that define the continuum limit of the theory directly with no need for a bare theory. We show how the self-consistency of the integral equations leads to the determination of the interaction vertices in the continuum limit. The inductive proof of the existence of a solution to the integral equations amounts to a proof of perturbative renormalizability, and it consists of nothing more than counting the scale dimensions of the interaction vertices. Universality is discussed within a context of the exact renormalization group.Comment: 26 pages, 2 figures, LaTeX2e with REVTEX

Off-shell renormalization of the abelian Higgs model in the unitary gauge

We discuss the off-shell renormalization properties of the abelian Higgs model in the unitary gauge. The model is not renormalizable according to the usual power counting rules. In this paper, however, we show that with a proper choice of interpolating fields for the massive photon and the Higgs particle, their off-shell Green functions can be renormalized. An analysis of the nature of the extra singularities in the unitary gauge is given, and a recipe for the off-shell renormalization is provided.Comment: 22 pages, 9 figures, late

Conformal invariance for Wilson actions

We discuss the realization of conformal invariance for Wilson actions using the formalism of the exact renormalization group. This subject has been studied extensively in the recent works of O. J. Rosten. The main purpose of this paper is to reformulate Rosten's formulas for conformal transformations using a method developed earlier for the realization of any continuous symmetry in the exact renormalization group formalism. The merit of the reformulation is simplicity and transparency via the consistent use of equation-of-motion operators. We derive equations that imply the invariance of the Wilson action under infinitesimal conformal transformations which are non-linearly realized but form a closed conformal algebra. The best effort has been made to make the paper self-contained; ample background on the formalism is provided.Comment: LaTeX 2e, 23 pages; Appendix A augmented, errors in Appendix C corrected (not reflected in the published version), typos corrected, references update

Connection on the theory space

By studying the geometric properties of correlation functions on the theory space, we are naturally led to a connection for the infinite dimensional vector bundle of composite fields over the theory space. We show how the short distance singularities of the theory are determined by the geometry of the theory space, i.e., the connection, beta functions, and anomalous dimensions. (This is a summary of the talk given at Strings '93 in Berkeley. The unnecessary blank lines in the original version have been removed in this revised version.)Comment: 4 pages (plain TeX), UCLA/93/TEP/2

The Energy-Momentum Tensor in Field Theory I

This is the first of three papers on the short-distance properties of the energy-momentum tensor in field theory. We study the energy-momentum tensor for renormalized field theory in curved space. We postulate an exact Ward identity of the energy-momentum tensor. By studying the consistency of the Ward identity with the renormalization group and diffeomorphisms, we determine the short-distance singularities in the product of the energy-momentum tensor and an arbitrary composite field in terms of a connection for the space of composite fields over theory space. We discuss examples from the four-dimensional $\phi^4$ theory. In the forthcoming two papers we plan to discuss the torsion and curvature of the connection.Comment: 25 pages, 2 PS figures, uses epsf, harvma

Integral equations for ERG

An application of the exact renormalization group equations to the scalar field theory in three dimensional euclidean space is discussed. We show how to modify the original formulation by J. Polchinski in order to find the Wilson-Fisher fixed point using perturbation theory.Comment: LaTeX2.e, 19 pages, 5 figures, based upon a talk presented at RG2005, Helsink

Gauge invariant composite operators of QED in the exact renormalization group formalism

Using the exact renormalization group (ERG) formalism, we study the gauge invariant composite operators in QED. Gauge invariant composite operators are introduced as infinitesimal changes of the gauge invariant Wilson action. We examine the dependence on the gauge fixing parameter of both the Wilson action and gauge invariant composite operators. After defining ``gauge fixing parameter independence,'' we show that any gauge independent composite operators can be made ``gauge fixing parameter independent'' by appropriate normalization. As an application, we give a concise but careful proof of the Adler-Bardeen non-renormalization theorem for the axial anomaly in an arbitrary covariant gauge by extending the original proof by A. Zee.Comment: 35 pages, no figur

Feynman graph solution to Wilson's exact renormalization group

We introduce a new prescription for renormalizing Feynman diagrams. The prescription is similar to BPHZ, but it is mass independent, and works in the massless limit as the MS scheme with dimensional regularization. The prescription gives a diagrammatic solution to Wilson's exact renormalization group differential equation.Comment: 17 pages, 5 figures, REVTeX4, revised with 2 more reference

Beta Functions in the Integral Equation Approach to the Exact Renormalization Group

We incorporate running parameters and anomalous dimensions into the framework of the exact renormalization group. We modify the exact renormalization group differential equations for a real scalar field theory, using the anomalous dimensions of the squared mass and the scalar field. Following a previous paper in which an integral equation approach to the exact renormalization group was introduced, we reformulate the modified differential equations as integral equations that define the continuum limit directly in terms of a running squared mass and self-coupling constant. Universality of the continuum limit under an arbitrary change of the momentum cutoff function is discussed using the modified exact renormalization group equations.Comment: 40 pages, 4 figures, LaTeX2e with REVTEX