Dynamical mass generation in pseudoquantum electrodynamics with Gross-Neveu interaction at finite temperature

We describe the dynamical mass generation in pseudoquantum electrodynamics (PQED) coupled to Gross-Neveu (GN) interaction, ($2+1$) dimensions, at both zero and finite temperatures. start with a gapless model show that, under particular conditions, dynamically generated emerges. In order do so, we use truncated Schwinger-Dyson equation, large-$N$ approximation, imaginary-time formalism. instantaneous-exchange approximation (the static regime), obtain two critical parameters, namely, number of fermions ${N}_{c}(T)$ coupling constant ${\ensuremath{\alpha}}_{c}(T)$ as function temperature cutoff $\mathrm{\ensuremath{\Lambda}}$, which must be provided by experiments. regime, find an analytical solution for $\mathrm{\ensuremath{\Sigma}}(p,T)$ well zero-external momentum $p=0$. continuum theory $\mathrm{\ensuremath{\Lambda}}=\ensuremath{\infty}$, where scale-invariance is respected, it shown that has any value $\ensuremath{\alpha}$. Furthermore, after calculating effective potential PQED, prove energetically favorable comparison massless phase. compare our results numerical tests good agreement found.