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Il Nuovo Cimento A (1965-1970)

, Volume 92, Issue 4, pp 347–363 | Cite as

Quantum corrections in Kaluza-Klein theory

  • R. Delbourgo
  • R. O. Weber
Article

Summary

We have examined some of the one-loop quantum corrections to the five-dimensional Kaluza-Klein model, which are due to the infinite number of massive spin-2 excitations, in order to discover how the tower of levels can affect the classical results. It turns out that quantities which vanish classically, such as 〈ϕ〉 and the mass of the scalar fieldϕ, receive finite contributions which are determined by the Planck radius. On the other hand, amplitudes such asϕ-ϕ scattering which are one-loop infinite, even when massive modes are disregarded, do not have their divergences ameliorated by the inclusion of the tower. We would conclude that a higher-dimensional model should be considered seriously as a candidate for a physical, quantized theory if (at the very least) the zero-mode truncation is already renormalizable, for only then are the entrained higher modes likely to produce finite corrections.

PACS

04.50. - Unified field theories and other theories of gravitation 

PACS

04.60. - Quantum theory of gravitation 

Riassunto

Sono state esaminate alcune delle correzioni quantiche ad un loop nel modello di Kaluza-Klein a 5 dimensioni, che sono dovute al numero infinito di eccitazioni a spin-2 dotate di massa per scoprire come la torre di livelli può condizionare i risultati classici. Risulta che le quantità che si annullano classicamente, come 〈ϕ〉 e la massa del campo scalareϕ, ricevono contributi finiti che sono determinati dal raggio di Planck. D’altra parte, ampiezze come lo scatteringϕ-ϕ che sono infinite ad un loop, anche quando si scartano i modi dotati di massa, non hanno divergenze migliorate dall’inclusione della torre. Concludiamo che un modello a piú dimensioni non si dovrebbe considerare seriamente come candidato per una teoria fisica quantizzata se (come minimo) il troncamento del modo zero è già rinormalizzabile, perché solo allora è probabile che i modi di ordine superiore producano correzioni finite.

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References

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Copyright information

© Società Italiana di Fisica 1986

Authors and Affiliations

  • R. Delbourgo
    • 1
  • R. O. Weber
    • 1
  1. 1.Department of PhysicsUniversity of TasmaniaHobartAustralia

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