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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Physik & Astronomie Theoretische Physik Supermathematics and its Applications in Statistical Physics
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Supermathematics and its Applications in Statistical Physics
Franz Wegner (Broschiert, Englisch)
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Beschreibung
This 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. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
26.03.2016
Sprache
Englisch
EAN
9783662491683
Herausgeber
Springer Berlin
Serien- oder Bandtitel
Lecture Notes in Physics
Sonderedition
Nein
Autor
Franz Wegner
Seitenanzahl
374
Einbandart
Broschiert
Buch Untertitel
Grassmann Variables and the Method of Supersymmetry
Schlagwörter
Disordered systems, Supermatrices and superdeterminants, Supersymmetric and superreal matrices, Supersymmetric quantum mechanics, Random matrix theory, Nonlinear sigma model, Schäfer-Wegner parametrization
Thema-Inhalt
PHU - Mathematische Physik
GPFC - Kybernetik und Systemtheorie
Höhe
235 mm
Breite
15.5 cm
Hersteller: Springer Nature Customer Service Center GmbH, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com
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