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Scalar-particle production near the singularity in an anisotropic universe. I. Scalar field theory

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Il Nuovo Cimento B (1971-1996)

Summary

In this paper we will present the mathematical theory of a quantum scalar field in a Bianchi I anisotropic space-time; the main result is the explicit construction of a Hamiltonian formalism, based on techniques very similar to those of the Bose-gas theory, which leads to an unambiguous interpretation of the particle number operator. This formalism allows us to treat in aquantitative fashion the process of particle creation (or destruction) by a time-varying gravitational field near the initial singularity, taking into account the back-reaction of the particles created on the gravitational field itself.

Riassunto

Nel presente lavoro si presenta la teoria matematica di un campo scalare quantizzato in uno spazio-tempo anisotropo del tipo Bianchi I. Si costruisce un formalismo hamiltoniano, basato su tecniche molto simili a quelle usate nella teoria del gas di bosoni, capace di fornire un'interpretazione priva di ambiguità dell'operatore «numero di particelle». Il formalismo così costruito permette di studiare in modo quantitativo i processi di creazione (o distruzione) di particelle da parte di un campo gravitazionale rapidamente variabile nel tempo nei pressi della singolarità iniziale; è possibile, con l'aiuto di questo formalismo, tener conto della reazione delle particelle create sul campo gravitazionale medesimo.

Резюме

В этой статье мы предлагаем математическую теорию квантового скалярного поля в анизотропном пространстве-времени Бьянки И. Развивается гамильтонов формализм, основанный на технике очень близкой к технике теории Бозе-газа. Предложенный формализм приводит к однозначной интерпретации оператора числа частиц. Зтот формализм позволяет нам количесмвенно рассмотреть процесс рождения (или уничтожения) частиц в изменяющемся во времени гравитационном поле вблизи начальной сингулярности, учитывая обратную реакцию рожденных частиц на само гравитационное поле.

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  1. E. Pessa

    Present address: , Via Salaria per L'Aquila, 24/c, 02100, Rieti, Italia

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  1. Istituto di Fisica dell'Università, Roma

    E. Pessa

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Перевебено ребакцией.

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Pessa, E. Scalar-particle production near the singularity in an anisotropic universe. I. Scalar field theory. Nuov Cim B 37, 155–184 (1977). https://doi.org/10.1007/BF02726315

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