## Group Theory 5.3 Symmetrizers and Anti-Symmetrizers of Young Tableaux

We have introduced Young Tableaux, based on which we can define the irreducible symmetrizers. And we can construct the irreducible representations with these symmetrizers.

## Group Theory 5.2 Partitions and Young Diagrams

Gist   Partition of n: A partition of the integer n is a sequence of positive integers , satisfy: .

## Group Theory 5.1 One-Dimensional Representations

Symmetry group is just the permutation group, which has a non-trivial invariant subgroup consisting of all even permutations. (An even permutation is one which is equivalent to an even number of simple transpositions.) has a coset consisting of all odd permutations.

## Group Theory 4.3 Irreducible Operators and the Wigner-Echart Theorem

Irreducible tensors and Wigner-Eckart are important concepts in quantum mechanics, which I never master before and forget them now.

## Group Theory 4.2 The Reduction of Vectors – Projection Operators for Irrudcible Components

Based on a known irreducible representation, we can define the projection operators which can project any vectors into the irreducible space

## Group Theory 4.1 Irreducible Basis Vectors

Whenever a physical system possesses a symmetry, the basic solutions to the classical equations or the basis state vectors of the corresponding quantum mechanics equations problem are naturally classified according to the irreducible representations of the symmetry.

## Group Theory 3.8 Direct Product Representations, Clebsch-Gordan Coefficients

Direct Product Vector Space: Let and be inner product spaces and and be orthonormal basis in the two spaces respectively. Then the direct product space consists of all linear combinations of the orthonormal basis vector , which can be regarded as , such that (i) Inner product: ; (ii) where the complex number are the […]

## Spirited Away and The Secret of Kells

Spirited Away (2001) is written and directed by Hayao Miyazaki and produced by Studio Ghibli, which is my most favorite Cartoon movie. It tells the story of Chihiro Ogino (Hiiragi), a sullen ten-year-old girl who, while moving to a new neighborhood, enters the spirit world. After her parents are transformed into pigs by the witch […]

## More Is Different-P. Anderson’s Perspectives On Broken Symmetry And The Nature Of Hierarchical Structure Of Science

More is Different-Brekon Symmetry and the Nature of Hierarchical Structure of Science is a lecture given by Paul Anderson in 1967, and the expanded version was published in 1972. Anderson has demonstrated his views on the relationships between different fields of nature science-the hierarchical structure of science, and the broke symmetry was presented as a […]