Processing math: 100%
Skip to main content
MA PH 464 - Group Theory in Physics:
Lecture Notes
Vincent Bouchard
Contents
Prev
Up
Next
Contents
Prev
Up
Next
Front Matter
Motivation
References
1
Basic concepts of group theory
Groups
Subgroups
Direct product
Multiplication table
Presentation
Cosets
Conjugacy classes
The symmetric group
S
n
Normal subgroups
Quotient groups
Homomorphisms and isomorphisms
Fun stuff
2
Representation theory
Representations
Properties of representations
Unitary representations
Semisimplicity
Schur's lemmas
The great orthogonality theorem
Characters
Orthogonality for characters
Reducibility and decomposition
An example:
S
3
An example: the regular representation
Real, pseudoreal and complex representations
3
Applications
Crystallography
Quantum Mechanics
Coupled harmonic oscillators
The Lagrangian
4
Lie groups and Lie algebras
Lie groups
Rotations in two and three dimensions
Lie algebras
S
U
(
2
)
General remarks
5
Representation theory of Lie groups
Tensor representations of
S
O
(
3
)
Representations of Lie algebras and the adjoint representation
The highest weight construction for
s
u
(
2
)
Projective and spin representations
Tensor representations of
S
U
(
N
)
The Standard Model of particle physics and GUTs
Representations of the Lorentz group
Unitary representations of the Poincare group
Classification of simple Lie algebras
Authored in PreTeXt
🔗
Chapter
5
Representation theory of Lie groups
¶
5.1
Tensor representations of
S
O
(
3
)
5.2
Representations of Lie algebras and the adjoint representation
5.3
The highest weight construction for
s
u
(
2
)
5.4
Projective and spin representations
5.5
Tensor representations of
S
U
(
N
)
5.6
The Standard Model of particle physics and GUTs
5.7
Representations of the Lorentz group
5.8
Unitary representations of the Poincare group
5.9
Classification of simple Lie algebras
login