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Euler-Heisenberg action for fermions coupled to gauge and axial vectors: Hessian diagonalization, sector classification, and applications

Lucas Pereira de Souza

Abstract

We derive the closed-form one-loop Euler--Heisenberg effective actions for Dirac fermions coupled simultaneously to classical electromagnetic vector and massive pseudo-vector backgrounds within a controlled quasi-static approximation. Through complete diagonalization of the functional Hessian, we systematically delineate the parameter space into distinct sectors characterized by stability properties and spectral structure. We identify subspaces that encompass and extend results from previous studies into a broader class, admitting propagating axial fields as physically viable regimes; strikingly, we note a sector presenting chirality-asymmetric instability. This addresses long-standing questions regarding the well-defined nature, diagonalizability, and stability of the model. From the effective action, we derive novel nonperturbative pair-production rates for simultaneously propagating electromagnetic and axial vector backgrounds; remarkably, we find pronounced vacuum stabilization compared to previous results. Furthermore, we demonstrate that this framework allows for a unified derivation of the chiral anomaly structures in the general case and show that the electromagnetic coupling induces instanton-like configurations for the axial field, even when it is not a fundamental gauge field. As a proof-of-concept, we analyze a cosmological toy model of baryogenesis driven by an axial vector, providing numerical estimates that support the viability of this hypothesis. Additionally, we outline qualitative predictions for Weyl/Dirac semi-metals and briefly discuss potential applications in related phenomena, such as the Strong-CP problem.

Euler-Heisenberg action for fermions coupled to gauge and axial vectors: Hessian diagonalization, sector classification, and applications

Abstract

We derive the closed-form one-loop Euler--Heisenberg effective actions for Dirac fermions coupled simultaneously to classical electromagnetic vector and massive pseudo-vector backgrounds within a controlled quasi-static approximation. Through complete diagonalization of the functional Hessian, we systematically delineate the parameter space into distinct sectors characterized by stability properties and spectral structure. We identify subspaces that encompass and extend results from previous studies into a broader class, admitting propagating axial fields as physically viable regimes; strikingly, we note a sector presenting chirality-asymmetric instability. This addresses long-standing questions regarding the well-defined nature, diagonalizability, and stability of the model. From the effective action, we derive novel nonperturbative pair-production rates for simultaneously propagating electromagnetic and axial vector backgrounds; remarkably, we find pronounced vacuum stabilization compared to previous results. Furthermore, we demonstrate that this framework allows for a unified derivation of the chiral anomaly structures in the general case and show that the electromagnetic coupling induces instanton-like configurations for the axial field, even when it is not a fundamental gauge field. As a proof-of-concept, we analyze a cosmological toy model of baryogenesis driven by an axial vector, providing numerical estimates that support the viability of this hypothesis. Additionally, we outline qualitative predictions for Weyl/Dirac semi-metals and briefly discuss potential applications in related phenomena, such as the Strong-CP problem.

Paper Structure

This paper contains 18 sections, 109 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. The Electroaxial Theory
  3. Hessian Diagonalization and Sector Classification
  4. Extended-Quantum-Electrodynamics-type (EQED):
  5. Mixed-Transverse-type (MT):
  6. Non-anomalous-type (NonAnom):
  7. Teleparallel Rainich--Misner--Wheeler-type (TRMW):
  8. Other types:
  9. The Exact One-Loop Effective Action
  10. First class:
  11. Second class:
  12. Chiral Anomaly
  13. Phenomenological Applications
  14. Pair Production Rates
  15. Baryogenesis and Cosmology
  16. ...and 3 more sections

Figures (2)

  • Figure 1: Anomalous triangle diagrams corresponding to the (a) $\hbox{$S \hbox{$\to$} \gamma \gamma$}$ ($+$ permutations) and (b) $\hbox{$S \hbox{$\to$} SS$}$ processes.
  • Figure 2: Vacuum transition probabilities for an adiabatic laser pulse profile as described by laser, with pulse duration $\tau_{\rm pulse} = 80 \, fs$, and spatial extent $\sim \lambda = 0.15 \, nm$, according to (a) standard QED schwinger1951, (b) Eq. \ref{['eq:rate1']} for complexified fields, (c) Eq. \ref{['eq:maroto']} with $\eta S \sim 1 \times 10^{17} \, e V$, and (d) Eq. \ref{['eq:rate2b']} with $\eta B_S \sim 1 \times 10^{15} \, e V/m$. Note the pronounced vacuum stabilization when the axial vector is present, indicating that pseudo-vector backgrounds suppress Schwinger pair production.