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

Abstract

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