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Blub

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Someone wrote that "the action of an element of SO(3) corresponds to a physical rotation. The response of the (point!) particle is a rotation in the internal space (the representation space) of the particle". Is this true? I thought that the representation of a rotation in a vector space V is a rotation in the vector space V --- the basis in V is rotated, without the physical space to rotate. Can someone clear my confusion. I would be so grateful.