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The title says it. why is a spinor not a tensor? I know the transformation rules for a spinor but I cant see why it is not a tensor?

winnetou
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  • Tensors are defined by their transformation rules, hence they cannot be. Although both are sections of vector bundles, and there is a mapping from spinors to tensors. – Slereah Feb 22 '18 at 18:19
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    A tensor is made up out of direct products of the defining/vector representation, but a spinor is not: it constitutes a distinct representation not reachable from the vector one. So, typically, composing integral spin objects will never yield a half-integral object to you. – Cosmas Zachos Oct 18 '18 at 13:07
  • Wait: a spinor is defined as an element of a vector space (more precisely, as an element of a representation of a double cover of $SO(n)$). It is therefore a vector. Doesn't that make it a rank 0 tensor? – Voidt Sep 18 '23 at 10:34
  • Related https://physics.stackexchange.com/q/41211/226902 https://physics.stackexchange.com/q/766673/226902 https://physics.stackexchange.com/q/605707/226902 Possibile answer: https://physics.stackexchange.com/a/554283/226902 – Quillo Jan 14 '24 at 11:48

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