Supermathematics and its applications in statistical physics [electronic resource] : Grassmann variables and the method of supersymmetry / Franz Wegner.
Wegner, Franz, author.
2016
QC20
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Title Supermathematics and its applications in statistical physics [electronic resource] : Grassmann variables and the method of supersymmetry / Franz Wegner.
Author Wegner, Franz, author.
ISBN 9783662491706 (electronic book)
3662491702 (electronic book)
9783662491683
DOI https://doi.org/10.1007/978-3-662-49170-6
Published Heidelberg : Springer, 2016.
Language English
Description 1 online resource (xvii, 374 pages) : illustrations.
Item Number 10.1007/978-3-662-49170-6 doi
Call Number QC20
Dewey Decimal Classification 530.15
Summary 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.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Source of Description Online resource; title from PDF title page (SpringerLink, viewed March 30, 2016).
Series Lecture notes in physics ; 920.
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Part I Grassmann Variables and Applications
Part II Supermathematics
Part III Supersymmetry in Statistical Physics
Summary and Additional Remarks
References
Solutions
Index.

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