Properties of derivative expansion approximations to the renormalization group

Details Properties of derivative expansion approximations to the renormalization group Properties of derivative expansion approximations to the renormalization group

1996-10-02

arxiv.org/abs/hep-th/9610012v2

Int.J.Mod.Phys.B12:1343-1354,1998

Physics

High Energy Physics

High Energy Physics - Theory

(Minor touch ups of the lingo.) Invited talk at RG96, Dubna, Russia; 14 pages including 2 eps figures; uses LaTeX, epsf and sp

Scientific paper

10.1142/S0217979298000752

Approximation only by derivative (or more generally momentum) expansions, combined with reparametrization invariance, turns the continuous renormalization group for quantum field theory into a set of partial differential equations which at fixed points become non-linear eigenvalue equations for the anomalous scaling dimension $\eta$. We review how these equations provide a powerful and robust means of discovering and approximating non-perturbative continuum limits. Gauge fields are briefly discussed. Particular emphasis is placed on the r\^ole of reparametrization invariance, and the convergence of the derivative expansion is addressed.

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