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The results of renormalized perturbation theory, in QCD and other
quantum field theories, are ambiguous at any finite order, due to
renormalization-scheme dependence. The perturbative results depend
upon extraneous scheme variables, including the renormalization
scale, that the exact result cannot depend on. Such 'non-invariant
approximations' occur in many other areas of physics, too. The
sensible strategy is to find where the approximant is stationary
under small variations of the extraneous variables. This general
principle is explained and illustrated with various examples. Also
dimensional transmutation, RG equations, the essence of
renormalization and the origin of its ambiguities are explained in
simple terms, assuming little or no background in quantum field
theory. The minimal-sensitivity approach leads to 'optimized
perturbation theory,' which is developed in detail. Applications to
Re+e-, the infrared limit, and to the optimization of factorized
quantities, are also discussed thoroughly.
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