Summary
This paper presents a general expression for rotation operatorsR in terms of boson and fermion operators under the normal products. Then we have obtained the corresponding expressions ofR for two special cases of rotation representation: using Euler’s angles (αβγ) and using (χeψ). As an application, we have also obtained the expression for 〈jm′|R|jm〉 in terms of 〈1/2, ± 1/2|R|1/2, ± 1/2〉 and evaluated the matrix element 〈jm′|exp[−iψ·J]|jm〉.
Riassunto
Questo lavoro presenta un’espressione generale per gli operatori di rotazioneR nei termini degli operatori di bosoni e fermioni nei normali prodotti. Si sono quindi ottenute le espressioni corrispondenti diR per due casi speciali della rappresentazione di rotazione: usando gli angoli di Eulero (αβγ) ed usando (χeψ). Come applicazione si è anche ottenuta l’espressione per 〈jm′|R|jm〉 nei termini di 〈1/2, ±1/2|R|1/2, ±1/2〉 e si è valutato l’elemento di matrice 〈jm′|exp[−iψ·J]|jm〉.
Реэюме
В Этой статье приводится обшее выражение для операторов врашенияR в виде нормальных проиэведений боэонных и фермионных операторов. Эатем мы получаем соответствуюшие выраженияR для двух специальных случаев представления врашения: испольэуя углы Ёйлера (αβγ) и испольэуя χeψ. Как приложение, мы также получаем выражение для 〈jm′|R|jm〉 в терминах 〈1/2, ±±1/2|R| 1/2, ± 1/2) и оцениваем матричный Элемент 〈jm′|exp[−iψJ]|jm〉.
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References
J. Schwinger:Quantum Theory of Angular Momentum (Academic Press, New York, N. Y., 1965).
Fan Hong-yi andRuan Tu-nan:Kuxue Tong Bao (chinese),14, 1063 (1985).
J. R. Klauder andBo-Sture Skagerstam:Coherent States: Applications Physics and Mathematical Physics (World Scientific Publishing Co. Pte. Ltd., Singapore, 1985), p. 48.
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Hai, R., Yong-de, Z. Expression of rotation operators in form of normal products: the general theory and its applications. Il Nuovo Cimento B 103, 473–483 (1989). https://doi.org/10.1007/BF02753133
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DOI: https://doi.org/10.1007/BF02753133