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Heat kernel on lie groups and maximally symmetric spaces

Record Type:	Electronic resources : Monograph/item
Title/Author:	Heat kernel on lie groups and maximally symmetric spacesby Ivan G. Avramidi.
Author:	Avramidi, Ivan G.
Published:	Cham :Springer Nature Switzerland :2023.
Description:	xix, 190 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Kernel functions.
Online resource:	https://doi.org/10.1007/978-3-031-27451-0
ISBN:	9783031274510$q(electronic bk.)

Heat kernel on lie groups and maximally symmetric spaces
Avramidi, Ivan G.

Heat kernel on lie groups and maximally symmetric spaces[electronic resource] /by Ivan G. Avramidi. - Cham :Springer Nature Switzerland :2023. - xix, 190 p. :ill., digital ;24 cm. - Frontiers in mathematics,1660-8054. - Frontiers in mathematics..

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.

ISBN: 9783031274510$q(electronic bk.)

Standard No.: 10.1007/978-3-031-27451-0doiSubjects--Topical Terms:

214209
Kernel functions.

LC Class. No.: QA353.K47 / A97 2023

Dewey Class. No.: 515.9

Heat kernel on lie groups and maximally symmetric spaces
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505 0 $a 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.
520 $a 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.
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650 2 4 $a Mathematical Physics. $3 522725
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