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Il Nuovo Cimento B (1971-1996)

, Volume 93, Issue 1, pp 22–35 | Cite as

Consistent algebra for the constraints of quantum gravity

  • T. Christodoulakis
  • J. Zanelli
Article

Summary

In the previous paper, a proposal was advanced for the ordering of the operators Open image in new window μ that arise in Dirac's programme for the quantization of gravity. The resulting algebra, however, was found to contain an undesired anomalous operator. Here we present a minimal modification of the canonical commutation relations of gravity in order to ensure that covariance is maintained for noncommuting tensor operators. As a result of the modification, the algebra of the quantum operator constraints is found to close exactly as in the classical case.

PACS. 04.60

Quantum theory of gravitation 

PACS. 04.20.Fy

Canonical formalism Lagrangians and variational principles 

Riassunto

Nel precedente lavoro, si è evanzata una proposta per l'ordinamento degli operatori Open image in new window μ che si presentano nel programma di Dirac per la quantizzazione della gravità. Si è trovato che l'algebra risultante, comunque, conteneva un operatore anomalo indesiderato. Qui si presenta una modifica minima delle relazioni di commutazione canoniche della gravità per assicurare che la covarianza sia mantenuta per operatori tensoriali che non commutano. Come risultato della modifica, si trova che l'algebra dei vincoli dell'operatore quantistico si chiude esattamente come nel caso classico.

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References

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Copyright information

© Società Italiana di Fisica 1986

Authors and Affiliations

  • T. Christodoulakis
    • 1
  • J. Zanelli
    • 1
  1. 1.International Centre for Theoretical PhysicsTriesteItaly

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