This book, based on a graduate course given by the authors, is a
pedagogic and self-contained introduction to the renormalization
group with special emphasis on the functional renormalization
group. The functional renormalization group is a modern formulation
of the Wilsonian renormalization group in terms of formally exact
functional differential equations for generating functionals.
In Part I the reader is introduced to the basic concepts of the
renormalization group idea, requiring only basic knowledge of
equilibrium statistical mechanics. More advanced methods, such as
diagrammatic perturbation theory, are introduced step by step.
Part II then gives a self-contained introduction to the
functional renormalization group. After a careful definition of
various types of generating functionals, the renormalization group
flow equations for these functionals are derived. This procedure is
shown to encompass the traditional method of the mode elimination
steps of the Wilsonian renormalization group procedure. Then,
approximate solutions of these flow equations using expansions in
powers of irreducible vertices or in powers of derivatives are
given.
Finally, in Part III the exact hierarchy of functional
renormalization group flow equations for the irreducible vertices
is used to study various aspects of non-relativistic fermions,
including the so-called BCS-BEC crossover, thereby making the link
to contemporary research topics.
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