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--- advanced_tools:group_theory:representation_theory:tensor_product_representation [2023/02/25 19:25]
edi [Intuitive]
+++ advanced_tools:group_theory:representation_theory:tensor_product_representation [2023/02/25 19:28]
edi [Concrete]
@@ Line 11: / Line 11: @@
 **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 diagram below shows the defining representation of $SU(2)$ in its upper branch. To construct the tensor-product representation from 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.
+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 }}]