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The Epstein–Glaser method in scalar QFT models, with emphasis on the Compton effect

Gracia-Bondia, Jose M. The Epstein–Glaser method in scalar QFT models, with emphasis on the Compton effect. In: Simpozij Vladimir Jurko Glaser (20 October 2015 - 20 October 2015) Institut Ruđer Bošković, Zagreb, Hrvatska. (Unpublished)

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In almost every book of quantum field theory (QFT) one finds the neat formula for the scattering matrix. However, every practitioner knows that this is only the beginning of trouble, since the expression is not really defined: the (in)famous ultraviolet divergences of QFT originate in this fact. The virtue of Epstein-Glaser (EG) renormalization is that it deals with the problem by the methods of distribution theory, in such a way that all quantities appearing in the calculations are mathematically well defined. Formula for scattering matrix is perturbative, and its essential complications, as well as the method of their solution, are already evident at second order. So we shall proceed by a particularly instructive second-order case study, to wit, the Compton effect for spinless particles. Typically, at second order we encounter tree graphs as well as loop graphs. In EG renormalization, the distinction between them is to some extent erased. This is illustrated in the model at hand, leading to quantum gauge invariance. If time allows, we would also tackle the basic loop graph for vacuum polarization in our scalar electrodynamics model by the EG procedures.

Item Type: Unpublished conference/workshop items or lecture materials
Uncontrolled Keywords: quantum field theory; Epstein-Glaser
Depositing User: Kristina Ciglar
Date Deposited: 24 Feb 2016 13:32

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