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＜電子ブック＞
Heat Kernel on Lie Groups and Maximally Symmetric Spaces / by Ivan G. Avramidi
(Frontiers in Mathematics. ISSN:16608054)

版	1st ed. 2023.
出版者	(Cham : Springer Nature Switzerland : Imprint: Birkhäuser)
出版年	2023
本文言語	英語
大きさ	XIX, 190 p : online resource
著者標目	*Avramidi, Ivan G author SpringerLink (Online service)
件　名	LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) LCSH:Differential equations LCSH:Mathematical physics LCSH:Group theory FREE:Global Analysis and Analysis on Manifolds FREE:Differential Equations FREE:Mathematical Physics FREE:Group Theory and Generalizations
一般注記	Part I. Manifolds -- Chapter. 1. Introduction -- Chapter. 2. Geometry of Simple Groups -- Chapter. 3. Geometry of SU(2) -- Chapter. 4. Maximally Symmetric Spaces -- Chapter. 5. Three-dimensional Maximally Symmetric Spaces -- Part II: Heat Kernel -- Chapter. 6. Scalar Heat Kernel -- Chapter. 7. Spinor Heat Kernel -- Chapter. 8. Heat Kernel in Two Dimensions -- Chapter. 9. Heat Kernel on S3 and H3 -- Chapter. 10. Algebraic Method for the Heat Kernel -- Appendix A -- References -- Index This monograph studies the heat kernel for the spin-tensor Laplacians on Lie groups and maximally symmetric spaces. It introduces many original ideas, methods, and tools developed by the author and provides a list of all known exact results in explicit form – and derives them – for the heat kernel on spheres and hyperbolic spaces. Part I considers the geometry of simple Lie groups and maximally symmetric spaces in detail, and Part II discusses the calculation of the heat kernel for scalar, spinor, and generic Laplacians on spheres and hyperbolic spaces in various dimensions. This text will be a valuable resource for researchers and graduate students working in various areas of mathematics – such as global analysis, spectral geometry, stochastic processes, and financial mathematics – as well in areas of mathematical and theoretical physics – including quantum field theory, quantum gravity, string theory, and statistical physics HTTP:URL=https://doi.org/10.1007/978-3-031-27451-0

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