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advanced_tools:group_theory:representation_theory:tensor_product_representation
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Tensor Product Representation
Intuitive
Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party.
Concrete
Example
The diagram below shows the defining representation of $SU(2)$ in its upper branch. To construct the tensor-product representation of two copies of the defining representation, we let it act on the tensor-product space, $\mathbb{C}^2 \otimes \mathbb{C}^2$, as shown in the lower branch.
The resulting 4-dimensional representation is reducible, breaking up into a 1- and 3-dimensional irreducible representation. This is usually written as $\bf 2 \otimes 2 = 1 \oplus 3$.
This tensor-product representation is useful for describing a system of two spin-1/2 particles, in particular, to analyze its combined spin.
For a more detailed explanation of this diagram see Fun with Symmetry.
Abstract
The motto in this section is: the higher the level of abstraction, the better.
Why is it interesting?
advanced_tools/group_theory/representation_theory/tensor_product_representation.1677348703.txt.gz · Last modified: 2023/02/25 19:11 by edi
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