Axial Anomaly and Confinement in Two-dimensional QED: Singular Behavior of Vacuum Polarization at Threshold

2025/10/20 by Bailing Ma, Ma, Bailing, Chueng‐Ryong Ji +1
Physics and Astronomy · Computer Science · #Quantum Chromodynamics and Particle Interactions #Quantum and Classical Electrodynamics #Quantum Information and Cryptography

paper · pdf · doi:10.48550/arxiv.2510.17074

Abstract

Performing the perturbative calculation of the vacuum polarization amplitude in QED1+1, one finds an anomalous axial vector Ward identity. We note that the photon self-energy function displays a singularity in the 1+1D case, in stark contrast to the 3+1D case. We discuss the nature of this singularity and its physical implications from the perspectives of axial anomaly and confinement in two-dimensional QED. Computing the total cross section of e⁺e^-→ μ⁺μ^- and displaying the toy version of the R ratio in 1+1D with respect to the typical R ratio in 3+1D, we discuss the significance of using the dressed photon propagator in obtaining the finite cross section.

Citations

• Lectures on nonperturbative QCD ( Nonperturbative Topological Phenomena in QCD and Related Theories)

Related

• The axial anomaly and the conversion of gluons into photons
• The axial anomaly, dimensional regularization and Lorentz-violating QED
• Series expansion of the photon self-energy in QED and the photon anomalous magnetic moment
• Geometrizing the Anomaly
• QED Corrections in Unstable Vacuum