Gauge Invariance and Construction of the FermionBoson Vertex in QED3
Abstract
We study the specific role that the WardGreenTakahashi identity plays in the restoration of the gauge independence of the physical observables related to the phenomenon of Dynamical Symmetry Breaking in QED3, the chiral condensate and the fermion mass, in the framework of the SchwingerDyson equations (SDE). We see in the lack of gauge independence of the physical observables the necessity of including further gauge invariance constraints and study the gauge covariance of the Fermion Propagator (FP) through its LandauKhalatnikovFradkin transformation. From this we stress that 1) in order to achieve full gauge independence of the physical observables we must include the Full Vertex in the corresponding SDE for the FP, and 2) that Perturbation Theory (PT) is the only scheme where this gauge independence as well as all of the gauge invariance constraints are satisfied order by order. Therefore we carry out the construction of the fermionboson vertex taking PT as a guide upto the first order of approximation. We completely relate this vertex to the FP and propose a non perturbative form for it. Furthermore, we write this non perturbative vertex in a suitable form for its future implementation in similar studies.
 Publication:

arXiv eprints
 Pub Date:
 April 2004
 arXiv:
 arXiv:hepth/0404138
 Bibcode:
 2004hep.th....4138R
 Keywords:

 High Energy Physics  Theory
 EPrint:
 Ph. D. Thesis. English version. Originally submitted in spanish to the Universidad Michoacana de San Nicolas de Hidalgo, Mexico, September (2003). 124 pages. Uses axodraw, epsfig and latexsym. Spanish version available upon request