Skip to main content

Divergences and Anomalies in Kaluza-Klein Theories

  • Chapter
Quantum Gravity

Abstract

The quantization of Kaluza-Klein theories is analyzed from both the higher and lower dimensional standpoints. Equivalence is established using zeta-function techniques to handle the ultraviolet divergences. Certain special features emerge by compactifying an odd number of dimensions. For example, the resulting four-dimensional theory has vanishing anomalies.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Th. Kaluza, Sitzungsber, Preuss, Akad. Wiss. Berlin, Math. Phys.K1, 966 (1921)

    Google Scholar 

  2. O. Klein, Z. Phys.37, 895 (1926).

    Article  ADS  Google Scholar 

  3. J.M. Souriau, Nuovo Cimento30, 565 (1963)

    Article  MathSciNet  MATH  Google Scholar 

  4. W. Thirring, Acta Phys. Austr., Suppl.9, 256 (1972).

    Google Scholar 

  5. B.S. DeWitt, in “Dynamical Theory of Groups and Fields” (Gordon and Breach, New York, 1965), p. 139;

    MATH  Google Scholar 

  6. J. Rayski, Acta Phys. Polon.27, 947 (1965);

    MathSciNet  Google Scholar 

  7. J. Rayski, Acta Phys. Polon.28, 87 (1965);

    MathSciNet  Google Scholar 

  8. R. Kerner, Ann. Inst. Henry Poincaré, Sect. A9, 143 (1968);

    MathSciNet  Google Scholar 

  9. A. Trautman, Rep. Math. Phys.1, 29 (1970);

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. Y.M. Cho, J. Math. Phys.16, 2029 (1975);

    Article  ADS  Google Scholar 

  11. Y.M. Cho and P.G.O. Freund, Phys. Rev.D12, 1711 (1975);

    MathSciNet  ADS  Google Scholar 

  12. Y.M. Cho and P.S. Jang, Phys. Rev.D12, 3789 (1975).

    MathSciNet  ADS  Google Scholar 

  13. E. Witten, Nucl. Phys.B186, 412 (1981);

    Article  MathSciNet  ADS  Google Scholar 

  14. A. Salam and J. Strathdee, Trieste Preprint IC/81/211 (1981).

    Google Scholar 

  15. J. Scherk and J.H. Schwarz, Phys. LettersB57, 463 (1975);

    ADS  Google Scholar 

  16. E. Creamer and J. Scherk, Nucl. Phys.B103, 399 (1976);

    Article  MathSciNet  ADS  Google Scholar 

  17. J. Scherk and J.H. Schwarz, Phys. LettersB82, 60 (1979);

    ADS  Google Scholar 

  18. J. Scherk and J.H. Schwarz, Nucl. Phys.B153, 61 (1979);

    Article  MathSciNet  ADS  Google Scholar 

  19. E. Creamer, Preprint LPTENS 81/18 (1981)

    Google Scholar 

  20. E. Creamer, B. Julia and J. Scherk, Phys. LettersB76, 409 (1978);

    ADS  Google Scholar 

  21. E. Creamer and B. Julia, Phys. LettersB80, 48 (1978);

    ADS  Google Scholar 

  22. E. Creamer and B. Julia, Nucl. Phys.B159, 141 (1979).

    Article  ADS  Google Scholar 

  23. J. Scherk and J.H. Schwarz, Phys. LettersB82, 60 (1979).

    ADS  Google Scholar 

  24. E. Creamer and J. Scherk, Nucl. Phys.B108, 409 (1976);

    Article  MathSciNet  ADS  Google Scholar 

  25. E. Creamer and J. Scherk, Nucl. Phys.B118,61 (1977);

    Article  MathSciNet  ADS  Google Scholar 

  26. J.F. Luciana, Nucl. Phys.B135, 111 (1978)

    Article  ADS  Google Scholar 

  27. V. Ogievetsky and E. Sokatchev, DUBNA Preprint E2-80–139 (1980);

    Google Scholar 

  28. M.J. Duff and P. van Nieuwenhuizen, Phys. LettersB94, 179 (1980);

    ADS  Google Scholar 

  29. A. Aurilia, H. Nicolai and P.K. Townsend, Nucl. Phys.B176, 509 (1980).

    Article  MathSciNet  ADS  Google Scholar 

  30. P.G.O. Freund and M.A. Rubin, Phys. LettersB97, 233 (1980).

    MathSciNet  ADS  Google Scholar 

  31. B.S. DeWitt, see Reference 3.

    Google Scholar 

  32. B.S. DeWitt, Phys. Rep.C19, 295 (1975);

    Article  ADS  Google Scholar 

  33. S.M. Christensen, Phys. Rev.D14,2490 (1976);

    ADS  Google Scholar 

  34. J.S. Dowker and R. Critchley, Phys. Rev.D13, 3224 (1976);

    MathSciNet  ADS  Google Scholar 

  35. L.S. Brown, Phys. Rev.D15, 1469 (1977);

    ADS  Google Scholar 

  36. J.S. Dowker and R. Critchley, Phys. Rev.D16, 3390 (1977);

    ADS  Google Scholar 

  37. S.W. Hawking, Coamun. Math. Phys.55, 133 1977 ).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  38. D.J. Toms, Imperial College Preprint ICTP/81/82–11 (1981).

    Google Scholar 

  39. S.M. Christensen and M.J. Duff, Phys. LettersB76, 571 (1978);

    ADS  Google Scholar 

  40. S.M. Christensen and M.J. Duff, Nucl. Phys.B154, 301 (1979).

    Article  MathSciNet  ADS  Google Scholar 

  41. P.B. Gilkey, J. Diff. Geom,.10, 601 (1975);

    MathSciNet  MATH  Google Scholar 

  42. P.B. Gilkey, Compos. Math.38, 201 (1979).

    MathSciNet  MATH  Google Scholar 

  43. R.M. Wald, Conmaun. Math. Phys.70, 221 (1979).

    MathSciNet  ADS  Google Scholar 

  44. R. Seeley, Amer. J. Math.88, 781 (1966);

    Article  MathSciNet  MATH  Google Scholar 

  45. H.P. McKean and I.M. Singer, J. Diff. Geom.1, 43 (1967);

    MathSciNet  MATH  Google Scholar 

  46. P. Greiner, Arch. Rat. Mech. Annal.41, 163 (1971);

    Article  MathSciNet  MATH  Google Scholar 

  47. P.B. Gilkey, Adv. in Math.15, 334 (1975);

    Article  MathSciNet  MATH  Google Scholar 

  48. G. Kennedy, J. Phys.All, L173 (1978);

    Google Scholar 

  49. G. Kennedy, R. Critchley and J.S. Dowker, Ann. Phys. (N.Y.)125, 346 (1980).

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  MATH  Google Scholar 

  51. G. ’t Hooft and M. Veltman, Nucl. Phys.B44, 189 (1972);

    Article  ADS  Google Scholar 

  52. C.G. Bollini and J.J. Giambiaggi, Nuovo CimentoB12, 20 (1972);

    Google Scholar 

  53. J.F. Ashmore, Nuovo Cimento Lett.4, 289 (1972).

    Article  Google Scholar 

  54. C.W. Misner, K.S. Thorne and J.A. Wheeler, “Gravitation” (W.H. Freeman, San Francisco, 1973 ).

    Google Scholar 

  55. C.J. Isham, Proc. Roy. Soc. LondonA362, 383 (1978).

    MathSciNet  ADS  Google Scholar 

  56. S.D. Unwin, Phys. LettersB103, 18 (1981);

    MathSciNet  ADS  Google Scholar 

  57. A. Chockalingham, Ph.D. Thesis, Imperial College (1981).

    Google Scholar 

  58. E.T. Whittaker and G.N. Watson, “A Course of Modern Analysis”(Cambridge University Press, London, 1927 ).

    MATH  Google Scholar 

  59. G. Domokos and S. Kovesi-Domokos, Phys. Rev.D16, 3060 (1977).

    ADS  Google Scholar 

  60. C.J. Isham, Proc. Roy. Soc. LondonA364, 591 (1978);

    MathSciNet  ADS  Google Scholar 

  61. B.S. DeWitt, C.F. Hart and C.J. Isham, PhysicaA96, 197 (1979).

    MathSciNet  ADS  Google Scholar 

  62. K. Fujikawa, Phys. Rev. Letters42, 1195 (1979);

    Article  ADS  Google Scholar 

  63. S. Deser, M.J. Duff and C.J. Isham, Phys. Letters93B, 419 (1980).

    ADS  Google Scholar 

  64. H. Nicolai, Phys. LettersB84, 219 (1979).

    ADS  Google Scholar 

  65. B. Zumino, Nucl. Phys.B89, 535 (1975)

    Google Scholar 

  66. P.C. West, Nucl. Phys.B106, 219 (1976).

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Plenum Press, New York

About this chapter

Cite this chapter

Duff, M.J., Toms, D.J. (1984). Divergences and Anomalies in Kaluza-Klein Theories. In: Markov, M.A., West, P.C. (eds) Quantum Gravity. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-2701-1_27

Download citation

  • DOI: https://doi.org/10.1007/978-1-4613-2701-1_27

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4612-9678-2

  • Online ISBN: 978-1-4613-2701-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics