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Symmetry Methods in Physics
·
Module 2
Representation Theory and its Tools
1
Introduction to Group Representations
Define a group representation and identify when two representations are equivalent.
2
Reducible vs. Irreducible Representations
Distinguish between reducible and irreducible representations (irreps).
3
Schur's Lemmas and Intertwining Maps
State and apply Schur's lemmas to constrain intertwining maps between irreps.
4
Character Computation for Representations
Compute the character of a representation for each conjugacy class.
5
Decomposing Reducible Representations with the Great Orthogonality Theorem
Apply the great orthogonality theorem for characters to decompose a reducible representation into its irreducible components.
6
Character Tables from Orthogonality Relations
Construct the character table for a finite group using orthogonality relations.
7
Character Decomposition of Tensor Products
Decompose tensor product representations into irreps using characters.
8
Constructing Symmetry-Adapted Basis Vectors
Apply the projection formula to construct symmetry-adapted basis vectors for each irrep.
Previous module
Foundations of Group Theory
Next module
Point Groups and Molecular Symmetries