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Quantum field theory on curved space-time: an axiomatic approach

Квантовая теория поля в искривленном пространстве-времени: Аксиоматический подход

  • Published:
Il Nuovo Cimento A (1965-1970)

Summary

In this paper I stress the points of Wightman’s axiomatic formulation of a quantum field theory which are no longer valid on a curved space-time and attempt to modify them. In particular, the difficulties connected to the definition of covariant quantum states are interpreted as similar to a renormalization problem in flat space-time. Namely, it will be shown that there is no possibility of obtaining a unitaryS-matrix on a nonflat geometry. Some ways to avoid these problems and to define univocally a global quantum state space structure are then discussed.

Riassunto

In quest’articolo si danno le modificazioni necessarie per estendere la formulazione assiomatica di Wightman al caso di uno spazio-tempo curvo. In particolare si connette la difficoltà di definire globalmente la struttura degli stati quantistici covarianti alla mancanza di una matriceS unitaria. Si mostra che questo è connesso all’impossibilità di definire su un generico spazio-tempo curvo lo spazio delle «funzioni di test» come spazio di Schwartz. Allora si tenta di superare questo tipo di difficoltà definendo gli stati di una particella relativamente alla struttura asintotica di Geroch per una varietà riemanniana generica.

Резюме

В этой статье проводится необходимая модификация для обобщения аксиоматической формулировки квантовой теории поля Вайтмана на случай искривленного пространства-времени. В частности, трудности, связанные с определением ковариантных квантовых состояний, интерпретируются подобно проблеме перенормировки в плоском пространстве-времени. Показывается, что невозможно получить унитарнуюS-матрицу в неплоской геометрии. Затем обсуждаются некоторые способы обойти эти проблемы и определить глобальную структуру пространства квантовых состояний.

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  1. M. Martellini

    Present address: Istituto di Fisica dell’Università, Milano, Italia

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  1. Department of Physics, University of Alberta, Edmonton, Alta.

    M. Martellini

  2. Istituto Nazionale di Fisica Nucleare, Sezione di Pavia, Italia

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Martellini, M. Quantum field theory on curved space-time: an axiomatic approach. Nuov Cim A 67, 305–355 (1982). https://doi.org/10.1007/BF02902594

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