Summary
The properties of the tensor components of the transition operator with respect to an arbitrary compact group are investigated. The principal result is that as a consequence of unitarity the transition operator always has an invariant component whose imaginary part is nonnegative. The connection of this result with the consistency of phenomenological calculations in broken-symmetry models is discussed.
Riassunto
Si studiano le proprietà delle componenti tensoriali dell’operatore di transizione rispetto ad un arbitrario gruppo compatto. Il risultato principale è che, in conseguenza dell’unitarietà, l’operatore di transizione ha sempre una componente invariante la cui parte immaginaria è non negativa. Si discute come questo risultato sia connesso con la consistenza dei calcoli fenomenologici nei modelli di simmetria infranta.
Резюме
Исследуются свойства тензорных компонент оператора перехода по отношению к произвольной компактной группе. Как следствие унитарности, основной результат представляет, что оператор перехода всегда имеет инвариантную компоненту, чья мнимая часть не является отрицательной. Обсуждается связь этого результата с последовательностью феноменологических вычислений в моделях с нарушением симметрии.
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Literatur
SeeH. Harari:High-Energy Physics and Elementary Particles (I.A.E.A., Vienna, 1965), p. 353, for a review of the topic in the case ofSU 3. Some recent work on the completely symmetric limit ofSU 3 has been carried out byS. Meshkov andG. B. Yodh:Phys. Rev. Lett.,19, 603 (1967).
L. L. Foldy andR. F. Peierls:Phys. Rev.,130, 1585 (1963);D. Amati, L. L. Foldy, A. Stanghellini andL. Van Hove:Nuovo Cimento,32, 1685, (1964).
A. S. Wightman:PCT, Spin and Statistics, and All That (New York, 1964), p. 98, 99.
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This work was supported in part by the U.S. Atomic Energy Commission.
Traduzione a cura della Redazione.
Перевебено ребакцией.
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Kowalski, K.L. Tensor decomposition of the transition operator. Nuovo Cimento A (1965-1970) 57, 39–44 (1968). https://doi.org/10.1007/BF02824433
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DOI: https://doi.org/10.1007/BF02824433