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Quantization of scalar-spinor instanton

Квантование скалярно-спинорного « инстантона »

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Il Nuovo Cimento A (1965-1970)

Summary

A systematic quantization to the scalar-spinor instanton is given in a canonical formalism of Euclidean space. A basic idea is in the repair of the symmetries of theO 5-covariant system in the presence of the instanton. The quantization of the fermion is carried through in such a way that the fermion number should be conserved. Our quantization enables us to get well-defined propagators for both the scalar and the fermion, which are free from unphysical poles.

Riassunto

Si dà una quantizzazione sistematica dell’istantone spinoriale-scalare in un formalismo canonico dello spazio euclideo. L’idea di base sta nella riparazione della simmetria del sistema covariante secondoO 5 in presenza degli istantoni. La quantizzazione del fermione è effettuata in modo tale che il numero fermionico sia conservato. La nostra quantizzazione ci permette di ottenere propagatori ben definiti sia per lo scalare che per il fermione che sono liberi da poli non fisici.

Реэюме

В каноническом формалиэме звклидова пространства проводится систематическое квантование скалярно-спинорного « инстантона ». Основная идея эаключается в восстановлении симметрииO 5 ковариантной системы в присутствии ? инстантона ?. Квантование фермиона осушествляется таким обраэом, что число фермионов должно сохраняться. Наще квантование поэволяет получить пропа-гаторы для скаляра и для фермиона, которые свободны от нефиэических полюсов.

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References

  1. A. M. Polyakov:Phys. Lett.,59 B, 82 (1975); preprint NORDITA 76/33.

    Article  MathSciNet  ADS  Google Scholar 

  2. H. Inagaki:Phys. Lett.,69 B, 448 (1977).

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  3. Such repair of the symmetries might in general be called «tunnelling» when the amplitude is continued to Minkowski space. For the case of the BPST instanton, see ref. (1,3,4).

  4. G. ’t Hooft:Phys. Rev. Lett.,37, 8 (1976);Phys. Rev. D,14, 3432 (1976).

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  5. R. Jackiw andC. Rebbi:Phys. Rev. Lett.,37, 172 (1976);C. Callan, R. Dashen andD. Gross:Phys. Lett.,63 B, 334 (1976).

    Article  ADS  Google Scholar 

  6. S. Fubini:Nuovo Cimento,34 A, 521 (1976).

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  7. The five-dimensional formalism including fermions is found inV. de Alfaro andG. Furlan:Nuovo Cimento,34 A, 569 (1976);R. Jackiw andC. Rebbi:Phys. Rev. D,14, 517 (1976). The notations of the latter article are adopted henceforth.

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  8. Even forμ = 6 we get 〈χ + χ〉0=c +1 c 1=1/2π 2 due tog → 0, so that the situation is different from that of de Alfaro and Furlan (ref. (6)The five—dimensional formalism including fermions is found in ) where 〈χ + χ〉0=0.

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  9. For example, seeA. Jevicki:Nucl. Phys.,117 B, 365 (1976) and references cited therein.

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  10. See alsoN. Nielsen andB. Schroer:Nucl. Phys. 120 B, 621 (1977).

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  11. The author wants to thankF. Legovini for discussions about the construction of the Dirac matrix.

  12. P. A. M. Dirac:Lectures on Quantum Mechanics (New York, N. Y., 1964);A. Hanson, T. Regge andC. Teitelboim:Constrained Hamiltonian System (1974), to be published by the Accademia Nazionale dei Lincei, Roma.

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Authors and Affiliations

  1. International Centre for Theoretical Physics, Trieste, Italy

    H. Inagaki

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  1. H. Inagaki
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Supported in part by an Italian Government Fellowship.

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Inagaki, H. Quantization of scalar-spinor instanton. Nuov Cim A 42, 471–485 (1977). https://doi.org/10.1007/BF02730278

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  • DOI: https://doi.org/10.1007/BF02730278

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