Heat Kernel on Lie Groups and Maximally Symmetric Spaces
Autor: | Ivan G. Avramidi |
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EAN: | 9783031274510 |
eBook Format: | |
Sprache: | Englisch |
Produktart: | eBook |
Veröffentlichungsdatum: | 25.04.2023 |
Kategorie: | |
Schlagworte: | Heat Kernel;Heat Kernel Lie Groups;Heat Kernel Maximally Symmetric Spaces;Scalar Heat Kernel;Spinor Heat Kernel;Heat Kernel Algebraic Method;Spin tensor bundles;Hypergeometric operator |
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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.
?Dr. Ivan Avramidi is an accomplished researcher with more than 30 years of research experience in mathematical physics. He has a cutting-edge expertise in asymptotic analysis of partial differential equations on manifolds and the applications of these methods to quantum physics, differential geometry and financial mathematics. His research program spans such areas as global analysis, geometric analysis, mathematical physics, spectral geometry, differential geometry, quantum field theory, quantum gravity and financial mathematics. Dr. Avramidi has an extensive publication record including two books and more than 60 refereed papers.