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A generalization of tensor calculus and its applications to physics

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Abstract

Penrose's abstract index notation and axiomatic introduction of covariant derivatives in tensor calculus is generalized to fields with internal degrees of freedom. The result provides, in particular, an intrinsic formulation of gauge theories without the use of bundles.

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References

  1. Penrose, R. (1969). InBattele Rencontres, ed. DeWitt, C, and Wheeler, J. A., Benjamin, New York.

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  2. Penrose, R., and Rindler, W.Spinors, Twistors and Space-time Structure (to appear).

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Author notes

  1. Gary T. Horowitz (NATO Postdoctoral Fellow)

    Present address: Institute for Advanced Study, 08540, Princeton, New Jersey

Authors and Affiliations

  1. Physics Department, Syracuse University, 13210, Syracuse, New York

    Abhay Ashtekar (Alfred P. Sloan Fellow)

  2. Mathematical Institute, 24-29 St. Giles, OX1 3LB, Oxford, England

    Gary T. Horowitz (NATO Postdoctoral Fellow)

  3. Département de Mathématiques, Université de Clermont-Fd, 63170, Aubière, France

    Anne Magnon-Ashtekar

Authors
  1. Abhay Ashtekar
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  2. Gary T. Horowitz
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  3. Anne Magnon-Ashtekar
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Additional information

Work supported in part by the NSF Contract No. PHY-80-08155 and a grant from the Research and Equipment Fund, Syracuse University.

Supported in part by Crédits Ministériels, Tranche de Type C.

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Ashtekar, A., Horowitz, G.T. & Magnon-Ashtekar, A. A generalization of tensor calculus and its applications to physics. Gen Relat Gravit 14, 411–428 (1982). https://doi.org/10.1007/BF00756326

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  • DOI: https://doi.org/10.1007/BF00756326

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