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A Closed Formula for the Riemann Normal Coordinate Expansion

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Abstract

We derive an integral representation whichencodes all coefficients of the Riemann normalcoordinate expansion and also a closed formula for thosecoefficients.

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REFERENCES

  1. Fock, V. A. (1937). Sov. J. Phys. 12, 404.

    Google Scholar 

  2. Schwinger, J. (1951). Phys. Rev. 82, 664.

    Google Scholar 

  3. Fateev, V. A., Schwartz, A. and Tyupkin, Yu. (1976). Preprint FIAN-155, Moscow.

  4. Shifman, M. A. (1980). Nucl. Phys. B 173, 12.

    Google Scholar 

  5. Schmidt, M. G., and Schubert, C. (1993). Phys. Lett. B 318, 438.

    Google Scholar 

  6. Eisenhart, L. P. (1964). Riemannian Geometry (Princeton University Press, Princeton).

    Google Scholar 

  7. Alvarez-Gaumé, L., Freedman, D. Z., and Mukhi, S. (1981). Ann. Phys. (NY) 134, 85.

    Google Scholar 

  8. Lüscher, M. (1982). Ann. Phys. (NY) 142, 359.

    Google Scholar 

  9. Friedan, D. (1985). Ann. Phys. (NY) 163, 318.

    Google Scholar 

  10. Fridling, B. E., and van de Ven, A. E. M. (1986). Nucl. Phys. B 268, 719.

    Google Scholar 

  11. Atiyah, M. F., Bott, R., and Patodi, V. K. (1973). Inv. Math. 19, 279.

    Google Scholar 

  12. Bastianelli, F., and van Nieuwenhuizen, P. (1993). Nucl. Phys. B 389, 53.

    Google Scholar 

  13. Herglotz, G. (1925). Math. Ann. 93, 46.

    Google Scholar 

  14. O'Connor, D. J. (1985). PhD thesis, University of Maryland.

  15. Amsterdamski, P., Berkin, A. L., and O'Connor, D. J. (1989). Class. Quantum Grav. 6, 1981.

    Google Scholar 

  16. Dolgov, A. D., and Khriplovich, I. B. (1983). Gen. Rel. Grav. 15, 1032.

    Google Scholar 

  17. Avramidi, I. G. (1991). Nucl. Phys. B 355, 712.

    Google Scholar 

  18. van de Ven, A. E. M. (1998). Class. Quantum Grav. 15, 2311.

    Google Scholar 

  19. Fliegner, D., Haberl, P., Schmidt, M. G., and Schubert, C. (1998). Ann. Phys. (NY) 264, 51.

    Google Scholar 

  20. Müller, U. (1996). New Computing Techniques in Physics Research IV (World Scientific, Singapore), p. 193; (1996). Preprint DESY-96–154 (hep-th/9701124).

    Google Scholar 

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Muller, U., Schubert, C. & van de Ven, A.E.M. A Closed Formula for the Riemann Normal Coordinate Expansion. General Relativity and Gravitation 31, 1759–1768 (1999). https://doi.org/10.1023/A:1026718301634

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  • DOI: https://doi.org/10.1023/A:1026718301634

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