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Symmetries, Fields and Particles

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Author(s): N. Dorey, ed. Dexter Chua
Series: Cambridge Mathematical Tripos Part III Lecture Notes
Publisher: University of Cambridge
Year: 2016

Language: English
City: Cambridge
Tags: maths; mathematics; math; advanced; college; university; higher; further; pure; applied

Introduction
Lie groups
Definitions
Matrix Lie groups
Properties of Lie groups
Lie algebras
Lie algebras
Differentiation
Lie algebras from Lie groups
The exponential map
Representations of Lie algebras
Representations of Lie groups and algebras
Complexification and correspondence of representations
Representations of su(2)
New representations from old
Decomposition of tensor product of su(2) representations
Cartan classification
The Killing form
The Cartan basis
Things are real
A real subalgebra
Simple roots
The classification
Reconstruction
Representation of Lie algebras
Weights
Root and weight lattices
Classification of representations
Decomposition of tensor products
Gauge theories
Electromagnetism and U(1) gauge symmetry
General case
Lie groups in nature
Spacetime symmetry
Possible extensions
Internal symmetries and the eightfold way
Index