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<p>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 demands a critical value of the coupling for the dynamical generation of electron masses, encoded in the infrared behavior of the said 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 Schrödinger-like equation with an auxiliary potential barrier (well) subjected to boundary conditions for both high and low momenta. Then, the dynamical mass is associated with the zero mode of the corresponding Schrödinger-like operator and adheres to the Miransky scaling law, as expected.</p>

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Dynamical Mass Generation in QED: Miransky scaling and Schrödinger-like infinite well and barrier potentials supporting a bound state

  • 期刊论文

  • 发表日期：

    2025年9月22日

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  • Juan D. García-Muñoz,
  • A. Alfaro,
  • L. X. Gutiérrez-Guerrero,
  • A. Raya

摘要

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 demands a critical value of the coupling for the dynamical generation of electron masses, encoded in the infrared behavior of the said 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 Schrödinger-like equation with an auxiliary potential barrier (well) subjected to boundary conditions for both high and low momenta. Then, the dynamical mass is associated with the zero mode of the corresponding Schrödinger-like operator and adheres to the Miransky scaling law, as expected.