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Title
Heat kernel on lie groups and maximally symmetric spaces / Ivan G. Avramidi.
ISBN
9783031274510 (electronic bk.)
3031274512 (electronic bk.)
3031274504
9783031274503
Imprint
Cham, Switzerland : Birkhäuser, 2023.
Language
English
Description
1 online resource
Other Standard Identifiers
10.1007/978-3-031-27451-0 doi
Call Number
QA353.K47
Dewey Decimal Classification
515/.9
Summary
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.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed May 4, 2023).
Series
Frontiers in Mathematics Series.
Available in Other Form
Print version: 9783031274503
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.
