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The nonperturbative propagator and vertex in massless quenched QED_d

A. Bashir·R. Delbourgo
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Abstract

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.

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A. Bashir, R. Delbourgo. 2004-05-03. The nonperturbative propagator and vertex in massless quenched QED_d. https://doi.org/10.1088/0305-4470%2F37%2F25%2F011

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