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Resummation of mass terms in perturbative massless quantum field theory

Aste, Andreas. (2007) Resummation of mass terms in perturbative massless quantum field theory. Letters in Mathematical Physics, 81 (1). pp. 77-92.

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Abstract

The neutral massless scalar quantum field Phi in four- dimensional space- time is considered, which is subject to a simple bilinear self- interaction. Is is well- known from renormalization theory that adding a term of the form -m(2)/2 Phi(2) to the Lagrangean has the formal effect of shifting the particle mass from the original zero value to m after resummation of all two-leg insertions in the Feynman graphs appearing in the perturbative expansion of the S-matrix. However, this resummation is accompanied by some subtleties if done in a proper mathematical manner. Although the model seems to be almost trivial, is shows many interesting features which are useful for the understanding of the convergence behavior of perturbation theory in general. Some important facts in connection with the basic principles of quantum field theory and distribution theory are highlighted, and a remark is made on possible generalizations of the distribution spaces used in local quantum field theory. A short discussion how one can view the spontaneous breakdown of gauge symmetry in massive gauge theories within a massless framework is presented.
Faculties and Departments:05 Faculty of Science > Departement Physik > Former Organization Units Physics > Atomphysik (Trautmann)
UniBasel Contributors:Aste, Andreas W
Item Type:Article, refereed
Article Subtype:Book Review
Publisher:Springer
ISSN:0377-9017
Note:Publication type according to Uni Basel Research Database: Journal item -- The final publication is available at Springer see DOI link.
Language:English
Identification Number:
Last Modified:03 Nov 2016 10:51
Deposited On:03 Nov 2016 10:51

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