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An Introduction to some Mathematical Aspects of Scattering Theory in Models of Quantum Fields

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Scattering Theory in Mathematical Physics

Part of the book series: NATO Advanced Study Institutes Series ((ASIC,volume 9))

Abstract

We give an elementary introduction to some results, problems and methods of the recent study of scattering in models developed in connection with constructive quantum field theory.

As far as the main core of these lectures is concerned, we have made a deliberate effort to be understandable also for mathematicians having some notions of non-relativistic quantum mechanics but no specific previous knowledge of quantum field theory.

We introduce the Fock space, the free fields and the free Hamiltonian and discuss the singular perturbation problem posed by local relativistic interactions. Scattering theory is first discussed for the simplified cases of space cut-off interactions and of translation invariant interactions with persistent vacuum. We give then the Wightman-Haag-Ruelle axiomatic framework as a guide for the construction of models with local, relativistic interactions and of the corresponding scattering theory. The verification of the axioms is carried through in a class of models with local relativistic interactions in two-dimensional space-time.

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Authors and Affiliations

  1. Università di Napoli, Italy

    Sergio Albeverio

  2. Universitet i Oslo, Norway

    Sergio Albeverio

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  1. Sergio Albeverio
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  1. Dept. of Mathematics, University of Denver, Denver, Colo., USA

    J. A. Lavita  & J.-P. Marchand  & 

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© 1974 D. Reidel Publishing Company, Dordrecht-Holland

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Albeverio, S. (1974). An Introduction to some Mathematical Aspects of Scattering Theory in Models of Quantum Fields. In: Lavita, J.A., Marchand, JP. (eds) Scattering Theory in Mathematical Physics. NATO Advanced Study Institutes Series, vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-2147-0_14

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  • DOI: https://doi.org/10.1007/978-94-010-2147-0_14

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-2149-4

  • Online ISBN: 978-94-010-2147-0

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