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Titlebook: Supermathematics and its Applications in Statistical Physics; Grassmann Variables Franz Wegner Book 2016 Springer-Verlag Berlin Heidelberg

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書目名稱Supermathematics and its Applications in Statistical Physics
副標(biāo)題Grassmann Variables
編輯Franz Wegner
視頻videohttp://file.papertrans.cn/882/881883/881883.mp4
概述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 m
叢書名稱Lecture Notes in Physics
圖書封面Titlebook: Supermathematics and its Applications in Statistical Physics; Grassmann Variables  Franz Wegner Book 2016 Springer-Verlag Berlin Heidelberg
描述.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
出版日期Book 2016
關(guān)鍵詞Disordered systems; Supermatrices and superdeterminants; Supersymmetric and superreal matrices; Supersy
版次1
doihttps://doi.org/10.1007/978-3-662-49170-6
isbn_softcover978-3-662-49168-3
isbn_ebook978-3-662-49170-6Series ISSN 0075-8450 Series E-ISSN 1616-6361
issn_series 0075-8450
copyrightSpringer-Verlag Berlin Heidelberg 2016
The information of publication is updating

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More on Matricesentiable function . of a square matrix obeying the functional equation .(.).(.)?=?.(.) vanishes identically, or is a power of the superdeterminant. (3) The Berezinian of matrices with linearly dependent matrix elements is determined.
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Path Integrals for Fermions and Bosonss of the commutation relations and in the fact that bosonic states can be arbitrarily often occupied, whereas fermionic states allow only single occupation or no occupation. Consequently, bosons are described by commuting fields, and fermions by anticommuting fields. This formulation can be used for
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Dimers in Two Dimensionsd vertical directions. The question is: In how many different ways can the edges be covered by dimers so that, at each lattice point, exactly one edge is covered by a dimer. This dimer problem can be solved for a plain lattice, if no edges cross each other. As examples, we consider the square lattic
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More on Matrices for matrices with linearly dependent matrix elements. We find (1) If the ordinary part of a supermatrix is not degenerate, then it can be diagonalized by a similarity transformation. If it is degenerate, then even if it is hermitian, it can normally not be diagonalized. However, superreal hermitian
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