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.
Author(s): William A. Schwalm
Series: IOP Concise Physics
Publisher: IOP Publishing
Year: 2019
Language: English
Pages: 114
City: Bristol
PRELIMS.pdf
Preface
Acknowledgements
Author Biography
William A Schwalm
Introduction
Reference
CH001.pdf
Chapter 1 Generating functions
1.1 The basic idea
1.2 Elementary examples of generating functions
References
CH002.pdf
Chapter 2 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 groups
References
CH003.pdf
Chapter 3 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 operators
References
CH004.pdf
Chapter 4 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
References
CH005.pdf
Chapter 5 Concluding remarks
References
