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Progress in metric-affine gauge theories of gravity with local scale invariance

  • Part III. Invited Papers Dedicated To Peter Mittelstaedt
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Abstract

Einstein's general relativity theory describes very well the gravitational phenomena in themacroscopic world. In themicroscopic domain of elementary particles, however, it does not exhibit gauge invariance or approximate Bjorken type scaling, properties which are believed to be indispensible for arenormalizable field theory. We argue that thelocal extension of space-time symmetries, such as of Lorentz and scale invariance, provides the clue for improvement. Eventually, this leads to aGL(4, R)-gauge approach to gravity in which the metric and the affine connection acquire the status ofindependent fields. The Yang-Mills type field equations, the Noether identities, and conformal models of gravity are discussed within this framework. After symmetry breaking, Einstein's GR surfaces as an effective “low-energy” theory.

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References

  1. A. Einstein:The Meaning of Relativity, 5th ed. (Princeton University Press, Princeton, New Jersey, 1955).

    Google Scholar 

  2. A. Einstein: “Autobiographical notes,” in: P. A. Schilpp,Albert Einstein: Philosopher-Scientist (The Library of living Philosophers, Vol. VII) (Open Court, La Salle, Illinois, 1949).

    Google Scholar 

  3. D. H. Eckhardtet al., Phys. Rev. Lett. 60, 2567 (1988); M. E. Anderet al., Phys. Rev. Lett. 62, 985 (1989).

    Google Scholar 

  4. J. H. Taylor and J. M. Weisberg: “Further experimental tests of relativistic gravity using the binary pulsar PSR 1913 + 16,” preprint, Princeton University, submitted toAstrophys. J., 1989.

  5. J.-L. Staudenmann, S. A. Werner, R. Colella, and A. W. Overhauser,Phys. Rev. A 21, 1419 (1980).

    Google Scholar 

  6. G. Salvini and A. Silverman,Phys. Rep. 171, 231 (1989).

    Google Scholar 

  7. F. W. Hehl, J. D. McCrea, and E. W. Mielke, inExact Sciences and Their Philosophical Foundations—Vorträge des Internationalen Hermann-Weyl-Kongresses, Kiel 1985, W. Deppertet al., eds. (P. Lang-Verlag, Frankfurt a. M., 1988), p. 241. More references on metric-affine gravity are collected therein.

    Google Scholar 

  8. F. W. Hehl, J. D. McCrea, E. W. Mielke, and Y. Ne'eman, “Metric-affine gauge theory of gravity: Field equations, Noether identities, and conformal properties' in preparation, 1989.

  9. P. Mittelstaedt, in:Philosophie und Physik der Raum-Zeit, J. Audretsch and K. Mainzer, eds. (Bibliographisches Institut, Mannheim, 1988), p. 83.

    Google Scholar 

  10. H. Weyl,Sitzungsber. Königl. Preuss. Akad. Wiss. (Berlin), p. 465 (1918).

  11. H. A. Kastrup,Ann. Phys. (Leipzig) 9, 388 (1962).

    Google Scholar 

  12. H. Weyl,Naturwissenschaften 19, 49 (1931).

    Google Scholar 

  13. E. W. Mielke and F. W. Hehl, inExact Sciences and Their Philosophical Foundations—Vorträge des Internationalen Hermann-Weyl-Kongresses, Kiel 1985, W. Deppertet al., eds. (P. Lang-Verlag, Frankfurt a. M., 1988), p. 191.

    Google Scholar 

  14. H Weyl,Proc. Natl. Acad. Sci. USA 15, 323 (1929).

    Google Scholar 

  15. C. N. Yang and R. L. Mills,Phys. Rev. 96, 191 (1954).

    Article  Google Scholar 

  16. T.-P. Cheng and L.-F. Li,Gauge Theory of Elementary Particle Physics (Clarendon Press, Oxford, 1984).

    Google Scholar 

  17. N. Schmitz,Naturwissenschaften 75, 559 (1988).

    Google Scholar 

  18. E. Kröner, inPhysics of Defects, Les Houches, Session XXXV, 1980, R. Balianet al., eds. (North-Holland, Amsterdam, 1981), p. 215.

    Google Scholar 

  19. F. W. Hehl, G. D. Kerlick, and P. von der Heyde,Z. Naturforsch. 31a, 111, 524, 823 (1976);Phys. Lett. B 63, 446 (1976). E. A. Lord,Phys. Lett. A 65, 1 (1978).

    Google Scholar 

  20. F. W. Hehl, P. von der Heyde, G. D. Kerlick, and J. M. Nester,Rev. Mod. Phys. 48, 393 (1976).

    Article  Google Scholar 

  21. F. W. Hehl and J. D. McCrea,Found. Phys. 16, 265 (1986).

    Google Scholar 

  22. W. Kopczyński, J. D. McCrea, and F. W. Hehl,Phys. Lett. A 135, 89 (1989).

    Google Scholar 

  23. C. G. Callan, S. Coleman, and R. Jackiw,Ann. Phys. (N.Y.) 59, 42 (1970); S. Coleman:Aspects of Symmetry (Cambridge University Press, Cambridge, 1985).

    Google Scholar 

  24. Dj. Šijački and Y. Ne'eman,J. Math. Phys. 26, 2457 (1985); Y. Ne'eman and Dj. Šijački,Int. J. Mod. Phys. A 2, 1655 (1985).

    Google Scholar 

  25. Y. Ne'eman and Dj. Šijački,Phys. Rev. D 37, 3267 (1988).

    Google Scholar 

  26. Y. Dothan, M. Gell-Mann, and Y. Ne'eman,Phys. Lett. 17, 148 (1965).

    Google Scholar 

  27. E. W. Mielke:Geometrodynamics of Gauge Fields—On the Geometry of Yang-Mills and Gravitational Gauge Theories (Akademie-Verlag, Berlin, 1987).

    Google Scholar 

  28. P. Jordan:Schwerkraft und Weltall, 2nd ed. (Vieweg, Braunschweig, 1955).

    Google Scholar 

  29. C. Brans and R. Dicke,Phys. Rev. 124, 925 (1961).

    Google Scholar 

  30. F. Englert, C. Truffin, and R. Gastmans,Nucl. Phys. B 117, 407 (1976).

    Google Scholar 

  31. S. L. Adler,Rev. Mod. Phys. 54, 729 (1982).

    Google Scholar 

  32. M. Kaku,Nucl. Phys. B 203, 285 (1982).

    Google Scholar 

  33. S. Coleman and E. Weinberg,Phys. Rev. D 7, 1888 (1973).

    Google Scholar 

  34. P. Minkowski,Phys. Lett. B 71, 419 (1977).

    Google Scholar 

  35. Y. Ne'eman and Dj. Šijački,Phys. Lett. B 200, 489 (1988).

    Google Scholar 

  36. S. Weinberg,Rev. Mod. Phys. 61, 1 (1989).

    Google Scholar 

  37. V. Renčín:Renčins Schöne Neue Welt, G. Haaf., ed. (Meyster-Verlag, München, 1983).

    Google Scholar 

  38. J. H. Horne and E. Witten,Phys. Rev. Lett. 62, 501 (1989).

    Google Scholar 

  39. C. N. Yang,Phys. Rev. Lett. 33, 445 (1974).

    Article  Google Scholar 

  40. H. Cheng,Phys. Rev. Lett. 61, 2182 (1988).

    Google Scholar 

  41. H. Cheng and W. F. Kao: “Consequences of scale invariance,” MIT preprint, 1988.

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Authors and Affiliations

  1. Institute for Theoretical Physics, University of Cologne, D-5000, Köln 41, W. Germany

    Friedrich W. Hehl & Eckehard W. Mielke

  2. Department of Mathematical Physics, University College, Dublin 4, Ireland

    J. Dermott McCrea

  3. Dublin Institute for Advanced Studies, Dublin 4, Ireland

    J. Dermott McCrea

  4. Raymond and Beverley Sackler Faculty of Exact Sciences, Tel-Aviv University, 69978, Tel-Aviv, Israel

    Yuval Ne'eman

  5. Center for Particle Theory, University of Texas, 78712, Austin, Texas, USA

    Yuval Ne'eman

Authors
  1. Friedrich W. Hehl
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  2. J. Dermott McCrea
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  3. Eckehard W. Mielke
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  4. Yuval Ne'eman
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Additional information

Based on a plenary talk given by one of us (EWM) at the 53rd annual meeting of the Deutsche Physikalische Gesellschaft in Bonn on March 14, 1989.

Supported by the German-Israeli Foundation for Scientific Research and Development (GIF), Jerusalem and Munich.

Supported by the Deutsche Forschungsgemeinschaft (DFG), Bonn, project He 528/12-1.

Supported in part by DOE Grant DE-FG05-85-ER40200.

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Hehl, F.W., McCrea, J.D., Mielke, E.W. et al. Progress in metric-affine gauge theories of gravity with local scale invariance. Found Phys 19, 1075–1100 (1989). https://doi.org/10.1007/BF01883159

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  • DOI: https://doi.org/10.1007/BF01883159

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