Dynamical mass generation and critical behavior in pseudo-Proca quantum electrodynamics

TL;DR

This paper studies how gauge-field mass and other parameters influence chiral symmetry breaking in pseudo-Proca QED using Schwinger-Dyson equations, revealing critical thresholds and effects of anisotropy.

Contribution

It derives critical conditions for dynamical mass generation in PPQED considering gauge-field mass, flavor number, and anisotropy, advancing understanding of non-perturbative gauge dynamics.

Findings

Gauge-field mass suppresses dynamical mass generation.

Critical coupling depends on Fermi velocity and gauge mass.

Results connect to photon behavior in metamaterials.

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 $\alpha$, flavor number $N$, and ultraviolet cutoff $\Lambda$ determine the critical thresholds for chiral symmetry breaking in the reduced (2+1)D theory. We derive $\alpha_c(m,\Lambda)$ (quenched) and $N_c(m,\Lambda,g)$ (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 $\alpha^*_c \propto (1 + v_F^2/c^2)^{-1}$. These results clarify the non-perturbative dynamics of massive gauge fields in dimensionally reduced QED and connect to effective photon propagation in Proca metamaterials.