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On Rotor calculus, I

Published online by Cambridge University Press:  09 April 2009

H. A. Buchdahl
H. A. Buchdahl
Affiliation:
Australian National UniversityCanberra
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It 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.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 6 , Issue 4 , November 1966 , pp. 402 - 423
Copyright
Copyright © Australian Mathematical Society 1966

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