Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2006-11-28
JHEP 0703:041,2007
Physics
High Energy Physics
High Energy Physics - Phenomenology
43 pages, 11 figures; title and abstract slightly modified, several clarifying discussions added; final version to match the o
Scientific paper
10.1088/1126-6708/2007/03/041
In the context of scalar QED we derive the pinch technique self-energies and vertices directly from the Schwinger-Dyson equations. After reviewing the perturbative construction, we discuss in detail the general methodology and the basic field-theoretic ingredients necessary for the completion of this task. The construction requires the simultaneous treatment of the equations governing the scalar self-energy and the fundamental interaction vertices. The resulting non-trivial rearrangement of terms generates dynamically the Schwinger-Dyson equations for the corresponding Green's functions of the background field method. The proof relies on the extensive use of the all-order Ward-identities satisfied by the full vertices of the theory and by the one-particle-irreducible kernels appearing in the usual skeleton expansion. The Ward identities for these latter quantities are derived formally, and several subtleties related to the structure of the multiparticle kernels are addressed. The general strategy for the generalization of the method in a non-Abelian context is briefly outlined, and some of the technical difficulties are discussed.
Binosi Daniele
Papavassiliou Joannis
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