Heisenberg-Euler and the Quantum Dilogarithm
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917430797795328 |
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| author | Dunne, Gerald V. |
| author_facet | Dunne, Gerald V. |
| contents | A dispersion integral representation of the Heisenberg-Euler QED effective lagrangian is derived, with Faddeev's quantum dilogarithm as a generalized Borel kernel. The nonperturbative imaginary part of the effective lagrangian is expressed as the quantum dilogarithm, while the real part has the form of a dispersion integral involving both the quantum dilogarithm and its modular dual, a manifestation of electromagnetic duality. The Heisenberg-Euler effective lagrangian generates all one-loop QED scattering amplitudes in a constant external field, with the Lorentz invariants of the constant background electromagnetic field playing the role of the Mandelstam variables in conventional QED dispersion theory. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_14915 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Heisenberg-Euler and the Quantum Dilogarithm Dunne, Gerald V. High Energy Physics - Theory High Energy Physics - Phenomenology Mathematical Physics A dispersion integral representation of the Heisenberg-Euler QED effective lagrangian is derived, with Faddeev's quantum dilogarithm as a generalized Borel kernel. The nonperturbative imaginary part of the effective lagrangian is expressed as the quantum dilogarithm, while the real part has the form of a dispersion integral involving both the quantum dilogarithm and its modular dual, a manifestation of electromagnetic duality. The Heisenberg-Euler effective lagrangian generates all one-loop QED scattering amplitudes in a constant external field, with the Lorentz invariants of the constant background electromagnetic field playing the role of the Mandelstam variables in conventional QED dispersion theory. |
| title | Heisenberg-Euler and the Quantum Dilogarithm |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology Mathematical Physics |
| url | https://arxiv.org/abs/2512.14915 |