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Il Nuovo Cimento A (1965-1970)

, Volume 57, Issue 4, pp 638–648 | Cite as

A spinor approach to the Lanczos spin tensor

  • W. F. Maher
  • J. D. Zund
Article

Summary

The van der Waerden spinor corresponding to the Lanczos spin tensor is obtained and shown to be a spinor of type (3,1). This spinor, which directly appears in the spinor equivalents of the Wey1 and Bell-Robinson tensors, is intimately related to the Petrov classification. By using the dyad formalism of Newman and Penrose this relationship is explicitly exhibited in terms of the spin coefficients, the optical scalars, and the dyad component of the Lanczos spinor. A possible physical interpretation of the Lanczos spinor is proposed.

Keywords

Spin Tensor Weyl Spinor Petrov Type Optical Scalar Spin Coefficient 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Спиновный подход к спино-тензору Ланкзоша

Резюме

Получается спинор ван дер Вердена, соответствующий спинотензору Ланкзоша, и показывается, что он представляет спинор, типа (3, 1). Этот спинор, который появляется непосредственно в спинорных эквивалентах Вейля и тензоре Бел-Робинсона, тесно связан с классификацией Петрова. Используя диадный формализм Неймана и Пенроуза, это соотнощение точно выражается в терминах спиновых коэффициентов, оптических скаляров и диадных компннент спинора Ланкзоша. Предлагается возможная интерпретация спинора Ланкзоша.

Riassunto

Si ottiene lo spinore di van der Waerden corrispondente al tensore di spin di Lanczos e si dimostra che esso è uno spinore del tipo (3, 1). Questo spinore, che appare direttamente negli equivalenti spinoriali dei tensori di Weyle di Bel-Robinson, è connesso strettamente alla classificazione di Petrov. Usando il formalismo diadico di Newmann e Penrose, si scrive esplicitamente questa relazione in termini di coefficienti di spin, degli scalari ottici e delle componenti diadiche dello spinore di Lanczos. Si propone una possibile interpretazione fisica dello spinore di Lanczos.

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References

  1. (1).
    C. Lanczos:Rev. Mod. Phys.,34, 379 (1962).ADSMathSciNetCrossRefGoogle Scholar
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  5. (5).
    From now on we will omit the complex conjugate spinor equation since it is always analogous to the original equation.Google Scholar
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    F. A. E. Pirani:Brandeis Summer Institute in Theoretical Physics, vol.1 (1964). p. 249.Google Scholar
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    I. M. Gel'fand, R. A. Minlos andA. Ya. Shapiro:Representations of the Rotation and Lorentz Groups (London, 1963).Google Scholar
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    R. Penrose:Proc. Roy. Soc. London, A284, 159 (1965).ADSMathSciNetCrossRefGoogle Scholar
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    E. T. Newman andR. Penrose:Journ. Math. Phys.,3, 566 (1962).ADSMathSciNetCrossRefGoogle Scholar
  10. (12).
    For an interpretation of some of the other spin coefficients see (8).Google Scholar

Copyright information

© Società Italiana di Fisica 1968

Authors and Affiliations

  • W. F. Maher
    • 1
    • 2
  • J. D. Zund
    • 1
    • 2
  1. 1.Department of MathematicsNorth Carolina State UniversityRaleigh
  2. 2.Department of Pure MathematicsUniversity of CambridgeCambridge

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