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Abstract We consider reduced quantum electrodynamics ( RQED d γ , d e $$ {\mathrm{RQED}}_{d_{\gamma },{d}_e} $$ ) a model describing fermions in a d e -dimensional space-time and interacting via the exchange of massless bosons in d γ -dimensions (d e ≤ d γ ). We compute the two-loop mass anomalous dimension, γ m , in general RQED 4 , d e $$ {\mathrm{RQED}}_{4,{d}_e} $$ with applications to RQED4,3 and QED4. We then proceed on studying dynamical (parity-even) fermion mass generation in RQED 4 , d e $$ {\mathrm{RQED}}_{4,{d}_e} $$ by constructing a fully gauge-invariant gap equation for RQED 4 , d e $$ {\mathrm{RQED}}_{4,{d}_e} $$ with γm as the only input. This equation allows for a straightforward analytic computation of the gauge-invariant critical coupling constant, α c , which is such that a dynamical mass is generated for α r > α c , where α r is the renormalized coupling constant, as well as the gauge-invariant critical number of fermion flavours, N c , which is such that α c → ∞ and a dynamical mass is generated for N < N c . For RQED4,3, our results are in perfect agreement with the more elaborate analysis based on the resolution of truncated Schwinger-Dyson equations at two-loop order. In the case of QED4, our analytical results (that use state of the art five-loop expression for γ m ) are in good quantitative agreement with those obtained from numerical approaches. |
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