The Chiral Anomaly as Record Decoherence: Deriving the ABJ Coefficient from the K-Functional
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2026
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| _version_ | 1866901082336133120 |
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| author | Rosa, Joel Barrett |
| author_facet | Rosa, Joel Barrett |
| contents | <p>We show that the Adler-Bell-Jackiw chiral anomaly is a natural consequence of the record sector K_rec of the K-functional framework. Chirality (the eigenvalue of γ₅) is a record observable: it takes discrete values ±1, is measured in every weak interaction, and its indefiniteness is penalized by K_rec. In a background gauge field, the K_rec gradient drives the fermion density matrix toward states of definite chirality. The rate of this drive is the chirality decoherence rate λ_chiral = e²/(16π²), determined by the one-loop coupling of the fermion to the gauge field environment. Combined with the Atiyah-Singer index theorem, this yields ∂_μ⟨J^μ_5⟩ = (e²/16π²) F_μν F̃^μν. The derivation extends to non-abelian gauge fields: for SU(N) with fermions in representation R, λ_chiral = g²C(R)/(16π²), recovering the standard non-abelian anomaly. The Adler-Bardeen theorem (exactness at one loop) is proven rigorously from CPTP monotonicity and the quantum Cramér-Rao bound: the chirality variance decays geometrically under sequential CPTP maps, with a rate determined by the single-step quantum Fisher information. A new prediction is derived: the chiral anomaly is suppressed near the Bekenstein bound, with λ_eff = (e²/16π²)(1 − S/S_Bek), providing a natural timing mechanism for baryogenesis after the cosmological bounce.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19372645 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Chiral Anomaly as Record Decoherence: Deriving the ABJ Coefficient from the K-Functional Rosa, Joel Barrett chiral anomaly Adler-Bell-Jackiw anomaly quantum information decoherence record operators CPTP maps Atiyah-Singer index theorem Adler-Bardeen theorem quantum Fisher information Cramér-Rao bound Bekenstein bound baryogenesis K-functional density operators open quantum systems Quantum Field Theory Quantum Information Theory Mathematical Physics Particle Physics <p>We show that the Adler-Bell-Jackiw chiral anomaly is a natural consequence of the record sector K_rec of the K-functional framework. Chirality (the eigenvalue of γ₅) is a record observable: it takes discrete values ±1, is measured in every weak interaction, and its indefiniteness is penalized by K_rec. In a background gauge field, the K_rec gradient drives the fermion density matrix toward states of definite chirality. The rate of this drive is the chirality decoherence rate λ_chiral = e²/(16π²), determined by the one-loop coupling of the fermion to the gauge field environment. Combined with the Atiyah-Singer index theorem, this yields ∂_μ⟨J^μ_5⟩ = (e²/16π²) F_μν F̃^μν. The derivation extends to non-abelian gauge fields: for SU(N) with fermions in representation R, λ_chiral = g²C(R)/(16π²), recovering the standard non-abelian anomaly. The Adler-Bardeen theorem (exactness at one loop) is proven rigorously from CPTP monotonicity and the quantum Cramér-Rao bound: the chirality variance decays geometrically under sequential CPTP maps, with a rate determined by the single-step quantum Fisher information. A new prediction is derived: the chiral anomaly is suppressed near the Bekenstein bound, with λ_eff = (e²/16π²)(1 − S/S_Bek), providing a natural timing mechanism for baryogenesis after the cosmological bounce.</p> |
| title | The Chiral Anomaly as Record Decoherence: Deriving the ABJ Coefficient from the K-Functional |
| topic | chiral anomaly Adler-Bell-Jackiw anomaly quantum information decoherence record operators CPTP maps Atiyah-Singer index theorem Adler-Bardeen theorem quantum Fisher information Cramér-Rao bound Bekenstein bound baryogenesis K-functional density operators open quantum systems Quantum Field Theory Quantum Information Theory Mathematical Physics Particle Physics |
| url | https://doi.org/10.5281/zenodo.19372645 |