A Quadratic Curvature Lagrangian of Pawłowski and Raczka: A Finger Exercise with MathTensor

  • Efstratios Tsantilis
  • Roland A. Puntigam
  • Friedrich W. Hehl

Summary

Recently Pawłowski and Raczka (P&R) proposed a unified model for the fundamental interactions which does not contain a physical Higgs field. The gravitational field equation of their model is rederived under heavy use of the computer algebra system Mathematica and its package MathTensor.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Soleng, H. (1996): The Mathematica packages Carta. and Math Tensor for tensor analysis. In this book, pp. 210–230. Springer, BerlinGoogle Scholar
  2. 2.
    Pawlowski, M., Raczka, R. (1995): A Higgs-free model for fundamental interactions. Part I: Formulation of the model. In Bertrand, J. et al. (eds.): Modern Group Theoretical Methods in Physics ,pp. 221–232. Kluwer Academic, Dordrecht. (Also available from electronic archive Los Alamos, hep-ph/9503269)Google Scholar
  3. 3.
    Misner, C.W., Thorne, K.S., Wheeler, J.A. (1973): Gravitation. Freeman, San FranciscoGoogle Scholar
  4. 4.
    Bach, R. (1921): Zur Weylschen Relativitätstheorie und der Weylschen Erweiterung des Krümmungstensorbegriffs. Math. Zeitschr. 9, 110–135MathSciNetCrossRefGoogle Scholar
  5. 5.
    Schimming, R., Schmidt, H.-J. (1990): On the history of fourth order metric theories of gravitation. NTM-Schriftenr. Gesch. Naturw., Techn., Med. (Leipzig) 27, 41–48MathSciNetGoogle Scholar
  6. 6.
    Mielke, E.W. (1987): Geometrodynamics of gauge fields—On the geometry of Yang-Mills and gravitational gauge theories. Akademie-Verlag, BerlinMATHGoogle Scholar
  7. 7.
    Pawlowski, M., Raczka, R. (1994): A unified conformal model for fundamental interactions without dynamical Higgs field. Found. Phys. 24, 1305–1327ADSCrossRefGoogle Scholar
  8. 8.
    Parker, L., Christensen, S.M. (1994): Math Tensor: A system for doing tensor analysis by computer. Addison-Wesley, Redwood City, CAGoogle Scholar
  9. 9.
    Fiedler, B., Schimming, R. (1983): Singularity-free static centrally symmetric solutions of some fourth order gravitational field equations. Astron. Nachr. 304, 221–229ADSCrossRefGoogle Scholar
  10. 10.
    Perlick, V., Xu, C. (1995): Matching exterior to interior solutions in Weyl gravity: Comment on ’Exact vacuum solution to conformal Weyl gravity and galactic rotation curves’. Astrophys. J. 449, 47–51ADSCrossRefGoogle Scholar
  11. 11.
    Gregorash, D., Papini, D. (1980): Weyl-Dirac theory with torsion. Nuovo Cimento B55, 37–51MathSciNetADSCrossRefGoogle Scholar
  12. 12.
    Gregorash, D., Papini, D. (1980): Weyl-Dirac theory with torsion. II. Foundations and conservation equations. Nuovo Cimento B56, 21–38MathSciNetADSCrossRefGoogle Scholar
  13. 13.
    Hehl, F.W., McCrea, J.D., Mielke, E.W (1985): Weyl spacetimes, the dilation current and creation of gravitating mass by symmetry breaking. In Deppert, W., Hübner, K., Oberschelp, A., Weidemann, V. (eds.): Exact Scieces and their Philosophical Foundations—Vorträge des Internationalen Hermann-Weyl-Kongresses, Kiel 1985 ,pp. 241–310. P. Lang Verlag, Frankfurt a. M.Google Scholar
  14. 14.
    Hehl, F.W., McCrea, J.D., Mielke, E.W., Ne’eman, Y. (1995): Metric-affine gauge theory of gravity: Field equations, Noether identities, world spinors, and breaking of dilation invariance. Phys. Rep. 258, 1–171MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Efstratios Tsantilis
    • 1
  • Roland A. Puntigam
    • 1
  • Friedrich W. Hehl
    • 1
  1. 1.Institute for Theoretical PhysicsUniversity of CologneGermany

Personalised recommendations