Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2004-05-03
J.Phys.A37:6587-6598,2004
Physics
High Energy Physics
High Energy Physics - Phenomenology
13 pages, no figures, latex (uses IOP style files)
Scientific paper
10.1088/0305-4470/37/25/011
It is well known how multiplicative renormalizability of the fermion propagator, through its Schwinger-Dyson equation, imposes restrictions on the 3-point fermion-boson vertex in massless quenched quantum electrodynamics in 4-dimensions (QED$_4$). Moreover, perturbation theory serves as an excellent guide for possible nonperturbative constructions of Green functions. We extend these ideas to arbitrary dimensions $d$. The constraint of multiplicative renormalizability of the fermion propagator is generalized to a Landau-Khalatnikov-Fradkin transformation law in $d$-dimensions and it naturally leads to a constraint on the fermion-boson vertex. We verify that this constraint is satisfied in perturbation theory at the one loop level in 3-dimensions. Based upon one loop perturbative calculation of the vertex, we find additional restrictions on its possible nonperturbative forms in arbitrary dimensions.
Bashir Adnan
Delbourgo Robert
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