When I asked the question How do you subtract colors and divide them by irrational numbers? (Gluons) I got the answer that all these colors were vectors in Hilbert space, I want to know which vectors these colors are in Hilbert space, and what is Hilbert space.
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I think this question might be too broad: you're asking us to explain the basics of quantum mechanics. It's the sort of question you answer with a textbook, not in a few paragraphs. – Javier Nov 01 '19 at 13:20
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Are you familiar with the representations of SU(3)? – Yuzuriha Inori Nov 01 '19 at 13:22
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@Javier could you give me a link that would explain this to me? – Ekadh Singh - Reinstate Monica Nov 01 '19 at 13:22
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@YuzurihaInori I have read about it and found out it is related to gluons but do not understand it – Ekadh Singh - Reinstate Monica Nov 01 '19 at 13:23
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@Yay This might help you out https://physics.stackexchange.com/questions/10403/mathematically-what-is-color-charge – Yuzuriha Inori Nov 01 '19 at 13:24
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@YuzurihaInori I do not understand most of that, but thank you. – Ekadh Singh - Reinstate Monica Nov 01 '19 at 13:27
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You can think of the vectors you called red, blue, and green as basis vectors similar to $\hat x$, $\hat y$, and $\hat z$ in Euclidean space. They are what other vectors in the space get expressed in terms of. – G. Smith Nov 01 '19 at 16:31
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@G.Smith thank you for the help, that makes much more sense – Ekadh Singh - Reinstate Monica Nov 01 '19 at 21:52
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@G.Smith what space are the vectors green, blue, and red in? – Ekadh Singh - Reinstate Monica Nov 04 '19 at 18:47
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An abstract three-dimensional “color space”, unrelated to the three familiar spatial dimensions. It is the vector space for the fundamental representation $\mathbf{3}$ of $SU(3)$, the gauge group for QCD. The previous sentence may not be intelligible if you haven’t learned about Lie groups and their representations in vector spaces of various dimensions. – G. Smith Nov 04 '19 at 18:57
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@G.Smith I have not learned about them, I will study them now, thank you. – Ekadh Singh - Reinstate Monica Nov 05 '19 at 00:38