The conformal group, its casimir operators, and a four-position operator

Конформная группа, операторы Каэимира и четырехмерный оператор положениявремени


We are investigating a class of representations of the conformal group which are physically interesting because there exists a position-time 4-vector operator within them and, related to this, because they are used in field transformation laws. We show that in these representations the three Casimir operators of the group have a very simple interpretation; we discuss when these representations are irreducible and we show that this 4-position operator can be expressed in terms of the generators of the group.


Si stanno facendo ricerche su una classe di rappresentazioni del gruppo conforme, che sono fisicamente interessanti perché all’interno di esse esiste un operatore quadrivettoriale spazio-temporale e, in relazione con ciò, perché sono usate nelle leggi di trasformazione dei campi. Si mette in luce come in queste rappresentazioni i tre operatori di Casimir del gruppo abbiano un’interpretazione molto semplice; si discute quando queste rappresentazioni sono irriducibili; e si fa vedere che questo operatore quadriposizionale può essere espresso per mezzo dei generatori del gruppo.


Мы исследуем класс представлений конформной группы, которые представляют фиэический интерес, потому что сушествует оператор, определяюший четырех-вектор положения-времени, в зтих представлениях, и которые свяэаны с зтой группой, так как они испольэуются в эаконах преобраэования полей. Мы покаэываем, что в зтих представлениях три оператора Каэимира зтой группы имеют очень простую интерпретацию. Мы обсуждаем вопрос, когда зти представления являются неприводимыми. Мы покаэываем, что зтот оператор, определяюший четырех-вектор положения-времени, может быть выражен в терминах генераторов группы.

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Correspondence to S. Lagu or H. Laue.

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Research supported by the NRC.

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Lagu, S., Laue, H. The conformal group, its casimir operators, and a four-position operator. Nuov Cim A 20, 217–231 (1974).

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