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- W4231696170 abstract "This chapter develops a mathematical study of interacting quantum fields, using our new mathematical setting. The presentation given here is just a rough cleaning misicating basic ideas and methods which are a direct application of our theory of generalized functions as developed from chapter 3 to 11.The free fields are usually interpreted as vector valued distributions and following this interpretation we consider them in §11. 3 as vector valued generalized functions (elements of G*(R3, L(D1,))) whose values are unbounded operators on the Fock space. This interpretation leads us to the use (in §12. 1 and §12. 2 below) of the spectral theory of self adjoint operators on Hilbert spaces. In this way we obtain a weak solution of the interacting fields equation (§12. 2) but we do not succeed (in §12. 3) to explain the asymptotic approximation of the scattering operator by the (formal) renormalized perturbation series so the study in §12. 4 and §12. 5 (elimination of divergences) is only done on the misividual terms of the perturbation series without a justification of asymptotic approximation. In §12. 6 we discover that the free fields operators may be considered as generalized functions in G*(R3, L(D1)), i.e. whose values are bounded operators on the Fock space. This is very convenient since now one may define exponentials by the usual series (which are convergent when one deals with representatives) instead of the spectral theory above. This gives another construction of interacting fields operators and scattering operators (§12. 6 and §12, 7) and this method gives a result of asymptotic approximation (when the coupling constant tends to 0) of the scattering operator." @default.
- W4231696170 created "2022-05-12" @default.
- W4231696170 date "1984-01-01" @default.
- W4231696170 modified "2023-10-15" @default.
- W4231696170 title "Chapter 12 The Interacting Fields" @default.
- W4231696170 doi "https://doi.org/10.1016/s0304-0208(08)70994-0" @default.
- W4231696170 hasPublicationYear "1984" @default.
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