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How the factor of $1/2$ is purely conventional?

Lie Algebras are vector spaces, and the commutation relations in then are simply relations between elements of a basis of the vector space. Both in $SU(2)$, $SO(3)$, and in any other group, the ...
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How do you multiply a 4x1 spinor by a $SU(3)$ matrix?

Color and Dirac/spinor indices are different types of indices. E.g. the quark field carries both.
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2 votes
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What is the relationship between spinors and rotating motion geometrically?

In short: the spinning fields correspond to representations of the Lorentz group that we see arising for an isolated rotating body. Internal angular momentum as Lorentz group generator As a ...
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