Spinors are objects with a spinor index and in some very particular sense, a spinor index is exactly one-half of a vector index. So the generalized tensors may have either an integral number of indices or they may also have a half-integral number of indices! In a very clever sense, a spinor is a square root of a vector in the same sense as a vector is a square root of a tensor with two indices. How is it possible that we may break letters (indices) into pairs of letters?

— Why are there spinors?

— Lubos Motl

2012.07.30 Monday ACHK