03775nam 22006855 450 991071741880332120251009083542.09783031274510(electronic bk.)978303127450310.1007/978-3-031-27451-0(MiAaPQ)EBC7241391(Au-PeEL)EBL7241391(OCoLC)1377816879(DE-He213)978-3-031-27451-0(PPN)269655476(CKB)26523195700041(EXLCZ)992652319570004120230425d2023 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierHeat Kernel on Lie Groups and Maximally Symmetric Spaces /by Ivan G. Avramidi1st ed. 2023.Cham :Springer Nature Switzerland :Imprint: Birkhäuser,2023.1 online resource (197 pages)Frontiers in Mathematics,1660-8054Print version: Avramidi, Ivan G. Heat Kernel on Lie Groups and Maximally Symmetric Spaces Cham : Springer International Publishing AG,c2023 9783031274503 Includes bibliographical references and index.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.Frontiers in Mathematics,1660-8054Global analysis (Mathematics)Manifolds (Mathematics)Differential equationsMathematical physicsGroup theoryGlobal Analysis and Analysis on ManifoldsDifferential EquationsMathematical PhysicsGroup Theory and GeneralizationsGlobal analysis (Mathematics)Manifolds (Mathematics)Differential equations.Mathematical physics.Group theory.Global Analysis and Analysis on Manifolds.Differential Equations.Mathematical Physics.Group Theory and Generalizations.515.353515.9Avramidi Ivan G.1957-62541MiAaPQMiAaPQMiAaPQ9910717418803321Heat Kernel on Lie Groups and Maximally Symmetric Spaces3294466UNINA