By Leon A. Takhtajan
This ebook offers a accomplished therapy of quantum mechanics from a arithmetic standpoint and is out there to mathematicians beginning with second-year graduate scholars. as well as conventional issues, like classical mechanics, mathematical foundations of quantum mechanics, quantization, and the Schrodinger equation, this publication offers a mathematical remedy of structures of exact debris with spin, and it introduces the reader to sensible equipment in quantum mechanics. This contains the Feynman course essential method of quantum mechanics, integration in useful areas, the relation among Feynman and Wiener integrals, Gaussian integration and regularized determinants of differential operators, fermion structures and integration over anticommuting (Grassmann) variables, supersymmetry and localization in loop areas, and supersymmetric derivation of the Atiyah-Singer formulation for the index of the Dirac operator. ahead of this e-book, mathematicians may perhaps locate those issues in simple terms in physics textbooks and in really expert literature. This ebook is written in a concise variety with cautious recognition to express arithmetic formula of tools and effects. a variety of difficulties, from regimen to complex, aid the reader to grasp the topic. as well as delivering a basic wisdom of quantum mechanics, this e-book function a bridge for learning extra complicated subject matters in quantum physics, between them quantum box idea. must haves contain regular first-year graduate classes protecting linear and summary algebra, topology and geometry, and actual and complicated research.
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This e-book presents a complete remedy of quantum mechanics from a arithmetic point of view and is out there to mathematicians beginning with second-year graduate scholars. as well as conventional subject matters, like classical mechanics, mathematical foundations of quantum mechanics, quantization, and the Schrodinger equation, this e-book offers a mathematical remedy of structures of exact debris with spin, and it introduces the reader to useful tools in quantum mechanics.
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Quantum Mechanics for Mathematicians (Graduate Studies in Mathematics) by Leon A. Takhtajan