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On a semi-group approach to quantum field equations

О полугрупповом подходе к уравнениям квантовой теории поля

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Il Nuovo Cimento A (1965-1970)

Summary

Some field equations, suggested by the Thirring and Federbush models in quantum field theory are studied in a two-dimensional space-time. The theory of nonlinear semi-groups is used. The unknowns are functions whose values are bounded operators on a Hilbert space. The existence and uniqueness of the global solution is proved.

Riassunto

Si studiano in uno spaziotempo bidimensionale, usando la teoria dei semigruppi non lineari, varie equazioni di campo suggerite dai modelli di Thirring e di Federbush. Le incognite sono funzioni a valori operatori limitati su uno spazio di Hilbert. Si dimostra l’esistenza ed unicità della soluzione globale.

Реэюме

В двумерном пространстве-времени исследуются некоторые уравнения поля, предложенные в моделях Тирринга и Федербуща в квантовой теории поля. Испольэуется теория нелинейной полугруппы. Неиэвестными являются функции, чьи эначения представляют ограниченные операторы в гильбертовом пространстве. Докаэывается сушествование и единственность обшего рещения.

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References

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Author notes

  1. E. Salusti

    Present address: Sezione di Roma, Istituto Nazionale di Fisica Nucleare, Italy

  2. A. Tesei

    Present address: Istituto di Matematica dell’Università, Roma

Authors and Affiliations

  1. Istituto di Fisica dell’Università, Roma

    E. Salusti

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  1. E. Salusti
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  2. A. Tesei
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Salusti, E., Tesei, A. On a semi-group approach to quantum field equations. Nuov Cim A 2, 122–138 (1971). https://doi.org/10.1007/BF02723992

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  • DOI: https://doi.org/10.1007/BF02723992

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