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?

  • $\begingroup$ 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. $\endgroup$
    – Slereah
    Commented Feb 22, 2018 at 18:19
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    $\begingroup$ 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. $\endgroup$ Commented Oct 18, 2018 at 13:07
  • $\begingroup$ 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? $\endgroup$
    – Voidt
    Commented Sep 18, 2023 at 10:34


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