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Supermathematics and its Applications in Statistical Physics
Grassmann Variables and the Method of Supersymmetry
Taschenbuch von Franz Wegner
Sprache: 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.
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.
Über den Autor

Franz Wegner obtained his PhD from the Technical University in Munich in 1968 and, as postdoctoral researcher, has worked amongst others with Leo Kadanoff at Brown University in Providence, Rhode Island (USA). 1974 he was appointed professor of theoretical physics at Heidelberg University where he became a professor emeritus in 2006. Prof. Wegner is recipient of numerous prizes and awards, among them the Walter-Schottky prize (1976), the Max-Planck medal of the German Physical Society (1986), and most recently of the Lars-Onsager prize of the American Physical Society (2015).

Zusammenfassung

Authored by one of the pioneers in the field

Self-contained exposition of the mathematical foundations for physicists

Course-based, tutorial presentation of the subject matter

Includes supplementary material: [...]

Inhaltsverzeichnis
Part I Grassmann Variables and Applications.- Part II Supermathematics.- Part III Supersymmetry in Statistical Physics.- Summary and Additional Remarks.- References.- Solutions.- Index.
Details
Erscheinungsjahr: 2016
Fachbereich: Astronomie
Genre: Mathematik, Medizin, Naturwissenschaften, Physik, Technik
Rubrik: Naturwissenschaften & Technik
Thema: Lexika
Medium: Taschenbuch
Reihe: Lecture Notes in Physics
Inhalt: xvii
374 S.
3 s/w Illustr.
12 farbige Illustr.
374 p. 15 illus.
12 illus. in color.
ISBN-13: 9783662491683
ISBN-10: 3662491680
Sprache: Englisch
Herstellernummer: 978-3-662-49168-3
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Wegner, Franz
Auflage: 1st ed. 2016
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Lecture Notes in Physics
Verantwortliche Person für die EU: Books on Demand GmbH, In de Tarpen 42, D-22848 Norderstedt, info@bod.de
Maße: 235 x 155 x 22 mm
Von/Mit: Franz Wegner
Erscheinungsdatum: 26.03.2016
Gewicht: 0,593 kg
Artikel-ID: 104047905
Über den Autor

Franz Wegner obtained his PhD from the Technical University in Munich in 1968 and, as postdoctoral researcher, has worked amongst others with Leo Kadanoff at Brown University in Providence, Rhode Island (USA). 1974 he was appointed professor of theoretical physics at Heidelberg University where he became a professor emeritus in 2006. Prof. Wegner is recipient of numerous prizes and awards, among them the Walter-Schottky prize (1976), the Max-Planck medal of the German Physical Society (1986), and most recently of the Lars-Onsager prize of the American Physical Society (2015).

Zusammenfassung

Authored by one of the pioneers in the field

Self-contained exposition of the mathematical foundations for physicists

Course-based, tutorial presentation of the subject matter

Includes supplementary material: [...]

Inhaltsverzeichnis
Part I Grassmann Variables and Applications.- Part II Supermathematics.- Part III Supersymmetry in Statistical Physics.- Summary and Additional Remarks.- References.- Solutions.- Index.
Details
Erscheinungsjahr: 2016
Fachbereich: Astronomie
Genre: Mathematik, Medizin, Naturwissenschaften, Physik, Technik
Rubrik: Naturwissenschaften & Technik
Thema: Lexika
Medium: Taschenbuch
Reihe: Lecture Notes in Physics
Inhalt: xvii
374 S.
3 s/w Illustr.
12 farbige Illustr.
374 p. 15 illus.
12 illus. in color.
ISBN-13: 9783662491683
ISBN-10: 3662491680
Sprache: Englisch
Herstellernummer: 978-3-662-49168-3
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Wegner, Franz
Auflage: 1st ed. 2016
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Lecture Notes in Physics
Verantwortliche Person für die EU: Books on Demand GmbH, In de Tarpen 42, D-22848 Norderstedt, info@bod.de
Maße: 235 x 155 x 22 mm
Von/Mit: Franz Wegner
Erscheinungsdatum: 26.03.2016
Gewicht: 0,593 kg
Artikel-ID: 104047905
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