Lectures on selected topics in mathematical physics :further applications of Lie theory /

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"Version: 20190301"--Title page verso."A Morgan & Claypool publication as part of IOP Concise Physics"--Title page verso.Includes bibliographical references.1. Generating functions -- 1.1. The basic idea -- 1.2. Elementary examples of generating functions2. Groups -- 2.1. Introduction -- 2.2. Groups in general and finite groups in particular -- 2.3. Continuous groups -- 2.4. Group action and infinitesimal generators -- 2.5. Three examples of generating functions from one-parameter groups -- 2.6. Quantum oscillator example -- 2.7. Bessel functions by factoring -- 2.8. Bessel function generator -- 2.9. Multi-parameter Lie groups3. Lie algebras -- 3.1. Algebras -- 3.2. Associative algebras are essentially matrix algebras -- 3.3. Lie algebras are commutator subalgebras -- 3.4. Ideals and classification of complex Lie algebras -- 3.5. Levi's decomposition -- 3.6. The Killing form -- 3.7. Cartan subalgebra -- 3.8. Root geometry, Weyl group and brief comment on classification -- 3.9. Representations and Casimir operators4. Examples and applications -- 4.1. The algebra so(5) -- 4.2. Two-dimensional oscillator in a magnetic field -- 4.3. Generating functions for spherical harmonics -- 5. Concluding remarks.This book is a sequel to Lectures on Selected Topics in Mathematical Physics: Introduction to Lie theory with applications. This volume is devoted mostly to Lie groups. Lie algebras and generating functions, both for standard special functions and for solution of certain types of physical problems. It is an informal treatment of these topics intended for physics graduate students or others with a physics background wanting a brief and informal introduction to the subjects addressed in a style and vocabulary not completely unfamiliar.First year physics graduate students.Also available in print.Mode of access: World Wide Web.System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.Dr. William A Schwalm has been in the Department of Physics and Astrophysics at the University of North Dakota since 1980. His research is in condensed matter theory and application of mathematical methods to physical problems. He is also the author of Lectures on Selected Topics in Mathematical Physics: Elliptic functions and elliptic integrals, and Lectures on Selected Topics in Mathematical Physics: Introduction to Lie theory with applications.Title from PDF title page (viewed on April 1, 2019).

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: .,

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1 online resource (various pagings) :illustrations.

Language

English

ISBN/ISSN

9781643273501

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530.15/255

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Subject(s)

SCIENCE / Physics / Mathematical & Computational.
Mathematical physics.
Lie groups.
Lie algebras.

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William A. Schwalm.

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