Dynamical Mass Generation in QED: Miransky scaling and Schrödinger-like infinite well and barrier potentials supporting a bound state
Juan D. García-Muñoz, A. Alfaro, L. X. Gutiérrez-Guerrero, A. Raya
公開日: 2025/9/15
Abstract
In this study, we revisit the Schwinger-Dyson equation for the electron propagator in QED in three and four space-time dimensions. Our analysis addresses the non-perturbative phenomenon of dynamical chiral symmetry breaking, which requires a critical value of the coupling for the dynamical generation of electron masses, encoded in the infrared behavior of the corresponding Green function. With a minimalistic truncation of the infinite tower of equations and adopting standard assumptions, the resulting gap equation is linearized and transformed into a Schr\"odinger-like equation with an auxiliary potential barrier (or well) subjected to boundary conditions for both high and low momenta. The dynamical mass is then associated with the zero mode of the corresponding Schr\"odinger-like operator and follows the Miransky scaling law, as expected.