LEADER 04932nam 22007695 450 001 996466802803316 005 20200702014615.0 010 $a3-662-49170-2 024 7 $a10.1007/978-3-662-49170-6 035 $a(CKB)3710000000627586 035 $a(SSID)ssj0001661043 035 $a(PQKBManifestationID)16441786 035 $a(PQKBTitleCode)TC0001661043 035 $a(PQKBWorkID)14989712 035 $a(PQKB)11322471 035 $a(DE-He213)978-3-662-49170-6 035 $a(MiAaPQ)EBC6298752 035 $a(MiAaPQ)EBC5610825 035 $a(Au-PeEL)EBL5610825 035 $a(OCoLC)945692104 035 $z(PPN)258846496 035 $a(PPN)192769383 035 $a(EXLCZ)993710000000627586 100 $a20160325d2016 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aSupermathematics and its Applications in Statistical Physics$b[electronic resource] $eGrassmann Variables and the Method of Supersymmetry /$fby Franz Wegner 205 $a1st ed. 2016. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2016. 215 $a1 online resource (XVII, 374 p. 15 illus., 12 illus. in color.) 225 1 $aLecture Notes in Physics,$x0075-8450 ;$v920 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-662-49168-0 320 $aIncludes bibliographical references and index. 327 $aPart I Grassmann Variables and Applications -- Part II Supermathematics -- Part III Supersymmetry in Statistical Physics -- Summary and Additional Remarks -- References -- Solutions -- Index. 330 $aThis text presents the mathematical concepts of Grassmann variables and the method of supersymmetry to a broad audience of physicists interested in applying these tools to disordered and critical systems, as well as related topics in statistical physics. Based on many courses and seminars held by the author, one of the pioneers in this field, the reader is given a systematic and tutorial introduction to the subject matter. The algebra and analysis of Grassmann variables is presented in part I. The mathematics of these variables is applied to a random matrix model, path integrals for fermions, dimer models and the Ising model in two dimensions. Supermathematics - the use of commuting and anticommuting variables on an equal footing - is the subject of part II. The properties of supervectors and supermatrices, which contain both commuting and Grassmann components, are treated in great detail, including the derivation of integral theorems. In part III, supersymmetric physical models are considered. While supersymmetry was first introduced in elementary particle physics as exact symmetry between bosons and fermions, the formal introduction of anticommuting spacetime components, can be extended to problems of statistical physics, and, since it connects states with equal energies, has also found its way into quantum mechanics. Several models are considered in the applications, after which the representation of the random matrix model by the nonlinear sigma-model, the determination of the density of states and the level correlation are derived. Eventually, the mobility edge behavior is discussed and a short account of the ten symmetry classes of disorder, two-dimensional disordered models, and superbosonization is given. 410 0$aLecture Notes in Physics,$x0075-8450 ;$v920 606 $aPhysics 606 $aMathematical physics 606 $aStatistical physics 606 $aDynamical systems 606 $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013 606 $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000 606 $aComplex Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/P33000 606 $aMathematical Applications in the Physical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M13120 606 $aStatistical Physics and Dynamical Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/P19090 615 0$aPhysics. 615 0$aMathematical physics. 615 0$aStatistical physics. 615 0$aDynamical systems. 615 14$aMathematical Methods in Physics. 615 24$aMathematical Physics. 615 24$aComplex Systems. 615 24$aMathematical Applications in the Physical Sciences. 615 24$aStatistical Physics and Dynamical Systems. 676 $a514.224 700 $aWegner$b Franz$4aut$4http://id.loc.gov/vocabulary/relators/aut$0967417 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466802803316 996 $aSupermathematics and its Applications in Statistical Physics$92196294 997 $aUNISA