LEADER 05417nam 22008535 450 001 996466835603316 005 20200704062357.0 010 $a3-642-05094-8 024 7 $a10.1007/978-3-642-05094-7 035 $a(CKB)2560000000009144 035 $a(SSID)ssj0000399650 035 $a(PQKBManifestationID)11243883 035 $a(PQKBTitleCode)TC0000399650 035 $a(PQKBWorkID)10386130 035 $a(PQKB)10814679 035 $a(DE-He213)978-3-642-05094-7 035 $a(MiAaPQ)EBC3065222 035 $a(PPN)149080883 035 $a(EXLCZ)992560000000009144 100 $a20100427d2010 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aIntroduction to the Functional Renormalization Group$b[electronic resource] /$fby Peter Kopietz, Lorenz Bartosch, Florian Schütz 205 $a1st ed. 2010. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2010. 215 $a1 online resource (XII, 380 p. 68 illus.) 225 1 $aLecture Notes in Physics,$x0075-8450 ;$v798 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-642-05093-X 320 $aIncludes bibliographical references and index. 327 $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. 330 $aThis book, based on a graduate course given by the authors, is a pedagogic and self-contained introduction to the renormalization group with special emphasis on the functional renormalization group. The functional renormalization group is a modern formulation of the Wilsonian renormalization group in terms of formally exact functional differential equations for generating functionals. In Part I the reader is introduced to the basic concepts of the renormalization group idea, requiring only basic knowledge of equilibrium statistical mechanics. More advanced methods, such as diagrammatic perturbation theory, are introduced step by step. Part II then gives a self-contained introduction to the functional renormalization group. After a careful definition of various types of generating functionals, the renormalization group flow equations for these functionals are derived. This procedure is shown to encompass the traditional method of the mode elimination steps of the Wilsonian renormalization group procedure. Then, approximate solutions of these flow equations using expansions in powers of irreducible vertices or in powers of derivatives are given. Finally, in Part III the exact hierarchy of functional renormalization group flow equations for the irreducible vertices is used to study various aspects of non-relativistic fermions, including the so-called BCS-BEC crossover, thereby making the link to contemporary research topics. 410 0$aLecture Notes in Physics,$x0075-8450 ;$v798 606 $aPhysics 606 $aSolid state physics 606 $aSpectroscopy 606 $aMicroscopy 606 $aStatistical physics 606 $aDynamical systems 606 $aQuantum physics 606 $aMagnetism 606 $aMagnetic materials 606 $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013 606 $aSolid State Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P25013 606 $aSpectroscopy and Microscopy$3https://scigraph.springernature.com/ontologies/product-market-codes/P31090 606 $aComplex Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/P33000 606 $aQuantum Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19080 606 $aMagnetism, Magnetic Materials$3https://scigraph.springernature.com/ontologies/product-market-codes/P25129 615 0$aPhysics. 615 0$aSolid state physics. 615 0$aSpectroscopy. 615 0$aMicroscopy. 615 0$aStatistical physics. 615 0$aDynamical systems. 615 0$aQuantum physics. 615 0$aMagnetism. 615 0$aMagnetic materials. 615 14$aMathematical Methods in Physics. 615 24$aSolid State Physics. 615 24$aSpectroscopy and Microscopy. 615 24$aComplex Systems. 615 24$aQuantum Physics. 615 24$aMagnetism, Magnetic Materials. 676 $a515/.7 700 $aKopietz$b Peter$4aut$4http://id.loc.gov/vocabulary/relators/aut$061187 702 $aBartosch$b Lorenz$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aSchütz$b Florian$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a996466835603316 996 $aIntroduction to the Functional Renormalization Group$92430782 997 $aUNISA