Fermion Zero-Modes in the BPST Instanton Background: AtiyahSinger Index and Explicit Mode Construction
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2026
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| author | Morales Plaza, Manuel Martín |
| author_facet | Morales Plaza, Manuel Martín |
| contents | <p>Block R15.9.2.1 derives, within the TCFQ framework, the spectrum of fermion zero-modes of the Dirac operator iD/A coupled to the BPST instanton connection ABPST (sealed in R15.9.1, c2 = 1). The draft R15.9.2 was rejected by external audit for four structural deciencies: an incorrect intermediate computation of Aˆ in the index formula (R6), an unreliable radial ODE derivation (R4), an overly complex uniqueness argument (R7), and a missing explicit verication of the mode equation.<br>All four deficiencies are corrected here. The Atiyah-Singer index reduces directly to RS4 ch2(E) = −c2(E) = −1, since p1(S4) = 0 eliminates the Aˆ contribution in degree 4. The zero-mode is constructed with the correct spin-isospin coupled ansatz and<br>verified by direct substitution into iD/Aψ0 = 0. Uniqueness follows immediately from n− = − Index(iD/A) = 1 combined with n+ = 0 from the Weitzenböck estimate. The sealed result is: n+ = 0, n− = 1, Index(iD/ABPST) = −1.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19444942 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Fermion Zero-Modes in the BPST Instanton Background: AtiyahSinger Index and Explicit Mode Construction Morales Plaza, Manuel Martín <p>Block R15.9.2.1 derives, within the TCFQ framework, the spectrum of fermion zero-modes of the Dirac operator iD/A coupled to the BPST instanton connection ABPST (sealed in R15.9.1, c2 = 1). The draft R15.9.2 was rejected by external audit for four structural deciencies: an incorrect intermediate computation of Aˆ in the index formula (R6), an unreliable radial ODE derivation (R4), an overly complex uniqueness argument (R7), and a missing explicit verication of the mode equation.<br>All four deficiencies are corrected here. The Atiyah-Singer index reduces directly to RS4 ch2(E) = −c2(E) = −1, since p1(S4) = 0 eliminates the Aˆ contribution in degree 4. The zero-mode is constructed with the correct spin-isospin coupled ansatz and<br>verified by direct substitution into iD/Aψ0 = 0. Uniqueness follows immediately from n− = − Index(iD/A) = 1 combined with n+ = 0 from the Weitzenböck estimate. The sealed result is: n+ = 0, n− = 1, Index(iD/ABPST) = −1.</p> |
| title | Fermion Zero-Modes in the BPST Instanton Background: AtiyahSinger Index and Explicit Mode Construction |
| url | https://doi.org/10.5281/zenodo.19444942 |