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For example, sometimes one sees $SU(3)\otimes SU(2)\otimes U(1)$ instead of $SU(3)\times SU(2)\times U(1)$.

My understanding is the the product here is just the usual direct product (aka Cartesian product), which is completely different from a tensor product or Kronecker product which the $\otimes$ symbol is usually used for. So why is $\otimes$ often (especially in a high energy physics context) for the direct product--is it just historical convention or is there any deep reason?

Qmechanic
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Aqualone
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  • This is a common annoyance, cf. https://physics.stackexchange.com/q/447342/50583 and its linked questions. – ACuriousMind May 11 '19 at 22:37
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    I'm voting to close this question as off-topic because asking for the reasons for notation is off-topic here. If you are interested in the actual historical development, consider asking at [hsm.SE] instead. – ACuriousMind May 11 '19 at 22:38
  • I'm not interested in history. I am actually asking the question: is it just an annoying convention, or is there any physical or mathematical reason for it? I think this is a question that many people might have so it would be useful for it to be on the internet somewhere (and it's definitely of much more interest to people interested in physics than science historians). – Aqualone May 11 '19 at 22:50
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    @ACuriousMind I think this should be closed as a duplicate of the question you linked. It is essentially the same question, the OP is interested in terminology (not history per se), and there is no way for the OP to know whether it is a physics point or a pure terminology point a priori (thus, the question). –  May 11 '19 at 22:55
  • @DvijMankad I agree, but the linked question (and linked questions therein) were about specific references or also focused on other things. The people who asked those questions seemed to be confused by the $\otimes$ vs $\times$ point, but those questions weren't mainly about it. Someone in the future who is confused about this would benefit more from the present question than those questions, imho. – Aqualone May 11 '19 at 23:01
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    What would one even mean by the tensor product of noncommutative groups? – WillO May 12 '19 at 00:23
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    It’s because the tensor product looks more “mathy”, so it presumably makes the writer look cooler. – knzhou May 12 '19 at 01:12

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