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Invariant four-vectors underE(3, 1) and some of its subgroups

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Abstract

Necessary and sufficient conditions ofinvariance on four-vectors under the Poincaré group E(3, 1) and its subgroups are exploited. As an example the Euclidean group in three dimensions and its subgroups are explicitly considered. Their invariant “potentials” are systematically derived.

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References

  1. T. Fulton, R. Rohrlich, and L. Witten,Rev. Mod. Phys. 34, 442 (1962).

    Google Scholar 

  2. J. Beckers and M. Jaminon,Physica 94A, 165 (1978).

    Google Scholar 

  3. J. Beckers, M. Jaminon, and J. Serpe,J. Phys. A12, 1341 (1979).

    Google Scholar 

  4. H. Bacry, Ph. Combe, and J. L. Richard,Nuovo Cimento 67A, 267 (1970).

    Google Scholar 

  5. Ph. Combe and P. Sorba,Physica 80A, 271 (1975).

    Google Scholar 

  6. J. Beckers, J. Harnad, M. Perroud, and P. Winternitz,J. Math. Phys. 19, 2126 (1978).

    Google Scholar 

  7. J. Beckers and V. Hussin,J. Phys. A, 14, 317 (1981).

    Google Scholar 

  8. J. Beckers, J. Harnard, and P. Jasselette,J. Math. Phys. 21, 2491 (1981).

    Google Scholar 

  9. J. Beckers, J. Patera, M. Perroud, and P. Winternitz,J. Math. Phys. 18, 72 (1977).

    Google Scholar 

  10. H. A. Kastrup,Ann. Phys. Lpz. 9, 388 (1962); G. Mack and A. Salam,Ann. Phys. (N.Y.) 53, 174 (1969).

    Google Scholar 

  11. J. Patera, P. Winternitz, and H. Zassenhaus,J. Math. Phys. 16, 1597 (1974).

    Google Scholar 

  12. J. Patera, P. Winternitz, and H. Zassenhaus,Lect. Notes Phys. 79, 388 (1977).

    Google Scholar 

  13. H. Bacry, Ph. Combe, and P. Sorba,Rep. Math. Phys. 5, 145, 361 (1974).

    Google Scholar 

  14. E. P. Wigner,Ann. Math. 40, 149 (1939); J. Beckers and M. Jaspers,Ann. Phys. (N.Y.) 113, 237 (1978).

    Google Scholar 

  15. P. Moussa and R. Stora,Methods in Subnuclear Physics, vol. II, p. 265, N. Nikolic, ed. (Gordon and Breach, New York, 1968); J. Beckers,J. Math. Phys. 13, 915 (1972).

    Google Scholar 

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Beckers, J., Hussin, V. Invariant four-vectors underE(3, 1) and some of its subgroups. Found Phys 11, 881–893 (1981). https://doi.org/10.1007/BF00727105

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  • DOI: https://doi.org/10.1007/BF00727105

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