Summary
Segal’s rules for quantizing scalar and vector fields are extended to a quantization scheme for tensors of valences up to 5. The scheme fails when the valences are ≥6. It is not known whether this failure means that the whole approach is wrong or merely that there is some modification of the given expressions required.
Riassunto
Si estendono le leggi di Segal di quantizzazione dei campi scalari e vettoriali ad uno schema di quantizzazione per tensori con valenza fino a 5. Questo schema fallisce quando le valenze sono ≥6. Non si sa se questo insuccesso significhi che tutto l’approccio è sbagliato o semplicemente che è richiesta qualche modifica delle espressioni date.
Резюме
Правила Сегала для квантования скалярного и векторного оолей обобшаются на случай квантования тензоров с валентностью до 5. Предложенная схема неприменима, когда валентность больше или равна 6. Однако неизвестно, означает ли эта неприменимость, что подход в целом является неправильным или требуется некоторая модификация приведенных выражений.
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References
I. E. Segal:Ann. Math.,48, 930 (1977).
I. E. Segal:Journ. Math. Phys.,1, 468 (1960).
See, for example,F. J. Bloore:Report to Colloque CNRS, Geometrie Symplectique et Physique Mathematique, Aix-en-Provence (1973), p. 787.
P. Sommers:Journ. Math. Phys.,14, 787 (1973).
F. J. Bloore andI. R. Ghobrial:J. Phys. A,8, 1863 (1975).
F. J. Bloore andL. Routh:Nuovo Cimento,25 B, 78 (1975).
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Postal address from July 1977, c/o Tadros Rophael, 327, Ramsis Street, Cairo, Egypt.
Traduzione a cura della Redazione.
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Ghobrial, I.R., Naoum, R.S. On quantization of tensor fields. Nuov Cim B 43, 73–78 (1978). https://doi.org/10.1007/BF02728290
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DOI: https://doi.org/10.1007/BF02728290