Dynamical mass generation and critical behavior in pseudo-Proca quantum electrodynamics
Helio G. Barroso, Van Sérgio Alves, Leandro O. Nascimento
TL;DR
The paper investigates how a (3+1)D gauge-field mass in PPQED influences dynamical mass generation and chiral symmetry breaking in a dimensionally reduced (2+1)D setting. It uses non-perturbative Schwinger–Dyson equations in rainbow-quenched and rainbow-unquenched truncations, with dimensional reduction and anisotropy, deriving analytic expressions for critical parameters and identifying Miransky-type scaling near criticality. The results show that the Proca mass induces Yukawa-like screening that raises $α_c(m,Λ)$ and lowers $N_c(m,Λ,g)$; anisotropy shifts the threshold via $α_c^{*} = \frac{1}{2} \frac{(1 + m^2/Λ^2)^{3/2}}{1 + v_F^2/c^2}$, and a Miransky scaling regime emerges as the coupling approaches criticality. These findings illuminate the non-perturbative dynamics of massive gauge fields in reduced QED and suggest experimental analogues in Proca metamaterials to explore mass-controlled critical behavior.
Abstract
We investigate dynamical mass generation in pseudo-Proca quantum electrodynamics (PPQED) using Schwinger--Dyson equations in rainbow-quenched and unquenched approximations. The (3+1)D gauge-field mass $m$, fine-structure constant $α$, flavor number $N$, and ultraviolet cutoff $Λ$ determine the critical thresholds for chiral symmetry breaking in the reduced (2+1)D theory. We derive $α_c(m,Λ)$ (quenched) and $N_c(m,Λ,g)$ (unquenched), with the gauge-field mass suppressing dynamical mass generation via Yukawa screening. For anisotropic fermions with Fermi velocity $v_F \neq c$, the critical coupling scales as $α^*_c \propto (1 + v_F^2/c^2)^{-1}$. These results clarify the non-perturbative dynamics of massive gauge fields in dimensionally reduced QED and connect to effective photon propagation in Proca metamaterials.