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Titlebook: Mathematical Physics; A Modern Introductio Sadri Hassani Textbook 2013Latest edition The Editor(s) (if applicable) and The Author(s), under

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书目名称Mathematical Physics
副标题A Modern Introductio
编辑Sadri Hassani
视频video
概述Appreciated for its balance between rigor and physical application.New chapters on algebras, representation of Clifford algebras and spinors, fiber bundles, and gauge theories.Includes historical note
图书封面Titlebook: Mathematical Physics; A Modern Introductio Sadri Hassani Textbook 2013Latest edition The Editor(s) (if applicable) and The Author(s), under
描述.The goal of this book is to expose the reader to the indispensable role that mathematics plays in modern physics. Starting with the notion of vector spaces, the first half of the book develops topics as diverse as algebras, classical orthogonal polynomials, Fourier analysis, complex analysis, differential and integral equations, operator theory, and multi-dimensional Green‘s functions. The second half of the book introduces groups, manifolds, Lie groups and their representations, Clifford algebras and their representations, and fibre bundles and their applications to differential geometry and gauge theories..This second edition is a substantial revision with a complete rewriting of many chapters and the addition of new ones, including chapters on algebras, representation of Clifford algebras, fibre bundles, and gauge theories. The spirit of the first edition, namely the balance between rigour and physical application, has been maintained, as is the abundance of historical notes and worked out examples that demonstrate the "unreasonable effectiveness of mathematics" in modern physics..
出版日期Textbook 2013Latest edition
版次2
doihttps://doi.org/10.1007/978-3-319-01195-0
isbn_ebook978-3-319-01195-0
copyrightThe Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl
The information of publication is updating

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Spectral Decompositionthe operator may “look” quite complicated, while in others it may take a simple form. In a “special” basis, the operator may look the simplest: It may be a diagonal matrix. This chapter investigates conditions under which a basis exists in which the operator is represented by a diagonal matrix.
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Classical Orthogonal Polynomialsas solutions to differential equations arising in various physical problems. Such polynomials can be produced by starting with 1,.,..,… and employing the Gram-Schmidt process. However, there is a more elegant, albeit less general, approach that simultaneously studies most polynomials of interest to
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Fourier Analysisal modes, in electromagnetic theory and the frequency analysis of waves, in noise considerations and thermal physics, in quantum theory and the transformation between momentum and coordinate representations, and in relativistic quantum field theory and creation and annihilation operation formalism.
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Calculus of Residuesfinite integrals that are impossible to calculate otherwise. The derivation, application, and analysis of this tool constitute the main focus of this chapter. In the preceding chapter we saw examples in which integrals were related to expansion coefficients of Laurent series. Here we will develop a
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Separation of Variables in Spherical Coordinatesndent variable, leading to ordinary differential equations (ODEs). In other areas of physics in which extended objects such as fields are studied, variations with respect to position are also important. Partial derivatives with respect to coordinate variables show up in the differential equations, w
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