Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1998-02-06
Prog.Theor.Phys.Suppl.131:395-414,1998
Physics
High Energy Physics
High Energy Physics - Theory
Invited lectures at the Yukawa International Seminar '97. 20 pages including 6 eps figs. LaTeX. PTPTeX style files included
Scientific paper
10.1143/PTPS.131.395
These two lectures cover some of the advances that underpin recent progress in deriving continuum solutions from the exact renormalization group. We concentrate on concepts and on exact non-perturbative statements, but in the process will describe how real non-perturbative calculations can be done, particularly within derivative expansion approximations. An effort has been made to keep the lectures pedagogical and self-contained. Topics covered are the derivation of the flow equations, their equivalence, continuum limits, perturbation theory, truncations, derivative expansions, identification of fixed points and eigenoperators, and the role of reparametrization invariance. Some new material is included, in particular a demonstration of non-perturbative renormalizability, and a discussion of ultraviolet renormalons.
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