Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-23T14:53:42.191Z Has data issue: false hasContentIssue false
  • English
  • Français

On Rotor calculus, I

Published online by Cambridge University Press:  09 April 2009

H. A. Buchdahl
H. A. Buchdahl
Affiliation:
Australian National UniversityCanberra
Rights & Permissions [Opens in a new window]

Summary

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

References

Andrews, M., 1964, Thesis, Birmingham.Google Scholar
Buchdahi, H. A., 1962, Jour. Australian Math. Soc. 2, 369.CrossRefGoogle Scholar
Buchdahl, H. A., 1966, Jour. Australian Math. Soc. 6, 424.Google Scholar
Corson, E. M., 1953, Introduction to tensors, spinors, and relativistic wave equations, § 13. Blackie and Son.Google Scholar
Infeld, L. and van der Waerden, B. L., 1933, Sitz. Preu. A had. Wiss., 9, 380.Google Scholar
Jordan, P., Ehiers, J. and Kundt, W., 1960, Akad. Wiss. Lit. Mains. Abh. Math.-Nat. Kl. No. 2, 29.Google Scholar
Kurşunoğlu, B., 1961, Jour. Math. Phys. 2, 22.CrossRefGoogle Scholar
Peres, A., 1962, Jour. Math. Mech. 11, 61.Google Scholar
Petrov, A. Z., 1962, Recent developments in general relativity, p. 371. Pergamon.Google Scholar
Rastall, P., 1964, Nuovo Cim. 34, 1563.CrossRefGoogle Scholar
Schouten, J. A., 1954, Ricci Calculus (2nd ed.). Springer.CrossRefGoogle Scholar
Synge, J. L., 1958, Relativity: the special theory. Chap. 9, North-Holland.Google Scholar