On Rotor calculus, I

Abstract

SummaryIt is known that to every proper homogeneous Lorentz transformation there corresponds a unique proper complex rotation in a three-dimensional complex linear vector space, the elements of which are here called “rotors”. Equivalently one has a one-one correspondence between rotors and self- dual bi-vectors in space-time (w-space). Rotor calculus fully exploits this correspondence, just as spinor calculus exploits the correspondence between real world vectors and hermitian spinors; and its formal starting point is the definition of certain covariant connecting quantities τAkl which transform as vectors under transformations in rotor space (r-space) and as tensors of valence 2 under transformations in w-space.