Physics Notes by Jakob Schwichtenberg

Sidebar

group_theory:notions:spinor

Spinors

(Speak “spinnors”.)

“One could say that a spinor is the most basic sort of mathematical object that can be Lorentz-transformed.”

An introduction to spinors by Andrew M. Steane

Spinors arise as mathematical objects when one studies the representation theory of the Lorentz group.

The objects that transform under the $(\frac{1}{2},0)$ or $(0,\frac{1}{2})$ representation of the Lorentz group are called Weyl spinors, objects transform under the (reducible) $(\frac{1}{2},0) \oplus (0,\frac{1}{2})$ representation are called Dirac spinors.

Why are they interesting?

Spinors are the mathematical tool that we need to describe quantum fields (or particles) with spin $\frac{1}{2}$, i.e. fermions.