000 04083nam a22005655i 4500
001 978-3-642-05094-7
003 DE-He213
005 20160624101859.0
007 cr nn 008mamaa
008 100427s2010 gw | s |||| 0|eng d
020 _a9783642050947
_9978-3-642-05094-7
024 7 _a10.1007/978-3-642-05094-7
_2doi
050 4 _aQC5.53
072 7 _aPHU
_2bicssc
072 7 _aSCI040000
_2bisacsh
082 0 4 _a530.15
_223
100 1 _aKopietz, Peter.
_eauthor.
245 1 0 _aIntroduction to the Functional Renormalization Group
_h[electronic resource] /
_cby Peter Kopietz, Lorenz Bartosch, Florian Schütz.
260 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2010.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2010.
300 _aXII, 380p. 68 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Physics,
_x0075-8450 ;
_v798
505 0 _aI Foundations of the renormalization group -- Phase Transitions and the Scaling Hypothesis -- Mean-Field Theory and the Gaussian Approximation -- Wilsonian Renormalization Group -- Critical Behavior of the Ising Model Close to Four Dimensions -- Field-Theoretical Renormalization Group -- II Introduction to the functional renormalization group -- Functional Methods -- Exact FRG Flow Equations -- Vertex Expansion -- Derivative Expansion -- III Functional renormalization group approach to fermions -- Fermionic Functional Renormalization Group -- Normal Fermions: Partial Bosonization in the Forward Scattering Channel -- Superfluid Fermions: Partial Bosonization in the Particle–Particle Channel.
520 _aThis 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.
650 0 _aPhysics.
650 0 _aQuantum theory.
650 0 _aMathematical physics.
650 0 _aMagnetism.
650 1 4 _aPhysics.
650 2 4 _aMathematical Methods in Physics.
650 2 4 _aSolid State Physics.
650 2 4 _aSpectroscopy and Microscopy.
650 2 4 _aStatistical Physics, Dynamical Systems and Complexity.
650 2 4 _aQuantum Physics.
650 2 4 _aMagnetism, Magnetic Materials.
700 1 _aBartosch, Lorenz.
_eauthor.
700 1 _aSchütz, Florian.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642050930
786 _dSpringer
830 0 _aLecture Notes in Physics,
_x0075-8450 ;
_v798
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-05094-7
942 _2EBK2896
_cEBK
999 _c32190
_d32190