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I What kind of space is the space of spinors?

  1. May 27, 2016 #1
    Hi, i dont find much about spinor spaces. I can think in that spaces like a vector space above the field of complex numbers (a complex vector space)?

    sorry if what i saying is a non-sense, but i really want to understand better the math behind the concept of a spinor.

  2. jcsd
  3. May 27, 2016 #2

    Simon Bridge

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  4. May 27, 2016 #3
    Thanks Simon Bridge, im already seen before the wikipedia article but is the only place until now im read about spinor space as a complex vector space, because of this i had a doubt about the statement.

    (1) So complex vector space and spinor space are the same thing or spinor space are a particular case of a complex vector space?

    (2) Im still dont found a book which make that connection (about spinor space and complex vector space) can you indicate me one?

    thanks again
  5. May 27, 2016 #4


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  6. May 31, 2016 #5


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    Hey davi2686.

    You might want to look at the multiplication table / matrix structure to understand the algebra in specific detail.

    It also helps to look at complex numbers in terms of Grassmann algebras (exterior/inner products and bi-vectors) and in the different high level complex number algebras in a variety of dimension and understanding the geometric meaning of how the multiplication tables correspond to rotations and scaling in a particular space.

    The linear algebra decomposition of a space in terms of rotation, scaling, and possible translation can help visualize what is really going on.
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