Andrius: I am studying how spin representations manifest Bott periodicity. Metaphysically, I think this is giving me insight into the divisions of everything.
Spinors are defined as the elements of the vector space which is a representation of the spin group but not of the special orthogonal group. Spinors are thus part of the picture. But what actually interests me is how the structure of a spin representation depends on the dimension {$n$} of the spin group {$\textrm{Spin}(n)$}.
Spinors
Spinors are defined by what is done to them
Spinors are not defined by what they are. Instead, spinors are defined by what is done with them. Similarly, a "paperweight", a "piece of trash", a "sales item", a "hat" are all defined not by what they are but what is done with them.
Spinors are elements of a complex vector space
Spinors are elements of the vector spaces that are given by representations of spin groups. Currently, I am studying the Wikipedia article on Spin representation and the recipe it gives for building them.
- I am trying to understand spinors in the simplest case, the group {$\textrm{Spin}(3)\cong SU(2)$} which is the double cover of the special orthogonal group {$SO(3)$} of the rotations of the sphere.
- I should study Wikipedia: Spinors in three dimensions
- Later I should understand the spin statistics theorem
Here are my notes at Math4Wisdom: Spinors