advanced_tools:group_theory:representation_theory:tensor_product_representation
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advanced_tools:group_theory:representation_theory:tensor_product_representation [2023/02/25 19:26] edi [Concrete] |
advanced_tools:group_theory:representation_theory:tensor_product_representation [2023/03/19 21:46] (current) edi [Concrete] |
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| The resulting 4-dimensional representation is reducible, breaking up into a 1- and 3-dimensional irreducible representation. This is usually written as $\bf 2 \otimes 2 = 1 \oplus 3$. | 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. | + | This tensor-product representation is useful for describing a system of two spin-1/2 particles, in particular, to analyze the spin states of the combined system. |
| [{{ :advanced_tools:group_theory:representation_theory:su2_tensor_rep.jpg?nolink }}] | [{{ :advanced_tools:group_theory:representation_theory:su2_tensor_rep.jpg?nolink }}] | ||
| - | For a more detailed explanation of this diagram see [[https://esackinger.wordpress.com/|Fun with Symmetry]]. | + | For a more detailed explanation of this diagram see [[https://esackinger.wordpress.com/blog/lie-groups-and-their-representations/#su2_tensor_rep|Fun with Symmetry]]. |
| <tabbox Abstract> | <tabbox Abstract> | ||
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