Summary
An approach to the quantization of a free matter field in curved space-time is presented which takes advantage of the existence of infinitely many unitarily inequivalent Fock representations. The construction describes a particle creation mechanism, which, in the case of black-hole metric, has many properties of the Hawking process. The renormalizability of the theory is proved at the one-loop order. In this respect a crucial role is played by the contributions coming from the unitarily inequivalent representations of the canonical commutation relations.
Riassunto
Si presenta un approccio alla quantizzazione di un campo di materia libero in uno spazio-tempo curvo che si avvantaggia dell’esistenza di infinite rappresentazioni di Fock unitariamente inequivalenti. La costruzione descrive un meccanismo di creazione di particelle, che, nel caso di metrica di buco nero, ha molte proprietà del processo di Hawking. La rinormalizzabilità della teoria è provata all’ordine di un cappio. A questo proposito, i contributi dalle rappresentazioni delle relazioni di commutazione canoniche hanno un ruolo cruciale.
Резюме
Предлагается подход к квантованию свободного поля вещества в кривом пространстве-времени. В этом подходе существует бесконечно много унитарно неэквивалентных представлений фока. Предложенный формализм описывает механизм рождения частиц, который в случае метрики черной дыры обладает многими свойствами процесса Хокинга. Доказывается перенормируемость теории в однопетельном приближении. В этом отношении решаюшую роль играют вклады, происходящие от унитарно неэквивалентнхх представлений канонических коммутационных соотношений.
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Martellini, M., Sodano, P. & Vitiello, G. Vacuum structure for a quantum field theory in curved space-time. Nuov Cim A 48, 341–358 (1978). https://doi.org/10.1007/BF02781601
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DOI: https://doi.org/10.1007/BF02781601