If we consider the addition of orbital sngular momentum L and spin angular momentum S to produce the total angular momentum vector J, then J is a member of the vector space that is constructed by taking the tensor product of the vector spaces associated with L and S. Why don't we take direct sum of the vector spaces of L and S instead to construct the J-space? Why are we particularly using tensor product to combine the spaces?
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Qmechanic
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Anindita Sarkar
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Possible duplicates: https://physics.stackexchange.com/q/54896/2451 and links therein. – Qmechanic Jun 29 '23 at 08:55
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Related : Total spin of two spin- 1/2 particles. – Frobenius Jul 01 '23 at 13:00