I What kind of space is the space of spinors?

[davi2686]

Hi, i don't 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.

thanks

 

[Simon Bridge]

That is quite good sense actually - spinors form a vector space over the field of complex numbers... well done.
https://en.wikipedia.org/wiki/Spinor

 

[davi2686]

Thanks Simon Bridge, I am already seen before the wikipedia article but is the only place until now I am 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) I am still don't found a book which make that connection (about spinor space and complex vector space) can you indicate me one?

thanks again

 

[mathman]

https://en.wikipedia.org/wiki/Spinor

See above - spinors are a special kind of vector.

 

[chiro]

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.