Lectures on Selected Topics in Mathematical Physics: Further Applications of Lie Theory

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