Quantization on the Ideal Boundary and the Finite Widths of Resonances
Conformal field theory is quantized on the ideal boundary of a Riemann surface, and the effect on the widths of the resonances of the quantum states is evaluated. The resonances on a surface can be recast in terms of eigenfunctions of a differential operator on the Mandelstam plane. Cusps in this pl...
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2025-06-01
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| author | Simon Davis |
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| description | Conformal field theory is quantized on the ideal boundary of a Riemann surface, and the effect on the widths of the resonances of the quantum states is evaluated. The resonances on a surface can be recast in terms of eigenfunctions of a differential operator on the Mandelstam plane. Cusps in this plane, representing Landau singularities, reflect a divergence in the coupling. A cusp on the Riemann surface similarly causes a divergence in the scattering amplitude. The interpretation of the string diagram indicates that the self-interaction of the string in the vicinity of the cusp causes it to implode, which would require an infinite coupling. A consistent physical interpretation of cusps on surfaces requires supersymmetry. The study of unitary minimal models and N = 2 superminimal models indicates that there can exist a set of resonances at the cusps and ends of the surfaces. The uncertainty in the masses of six types of particles at a finite set of cusps is infinitesimal. Tachyon condensation on the ideal boundary would introduce an uncertainty in the mass of a charged particle. The widths of charged particle resonances at the ends of infinite-genus surfaces is not negligible and can be traced to the coupling with tachyons. |
| format | Article |
| id | doaj-art-81ded0e6a984454bb60fcd582031c923 |
| institution | DOAJ |
| issn | 2624-960X |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
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| series | Quantum Reports |
| spelling | doaj-art-81ded0e6a984454bb60fcd582031c9232025-08-20T03:16:38ZengMDPI AGQuantum Reports2624-960X2025-06-01722710.3390/quantum7020027Quantization on the Ideal Boundary and the Finite Widths of ResonancesSimon Davis0Research Foundation of Southern California, San Diego, CA 92115, USAConformal field theory is quantized on the ideal boundary of a Riemann surface, and the effect on the widths of the resonances of the quantum states is evaluated. The resonances on a surface can be recast in terms of eigenfunctions of a differential operator on the Mandelstam plane. Cusps in this plane, representing Landau singularities, reflect a divergence in the coupling. A cusp on the Riemann surface similarly causes a divergence in the scattering amplitude. The interpretation of the string diagram indicates that the self-interaction of the string in the vicinity of the cusp causes it to implode, which would require an infinite coupling. A consistent physical interpretation of cusps on surfaces requires supersymmetry. The study of unitary minimal models and N = 2 superminimal models indicates that there can exist a set of resonances at the cusps and ends of the surfaces. The uncertainty in the masses of six types of particles at a finite set of cusps is infinitesimal. Tachyon condensation on the ideal boundary would introduce an uncertainty in the mass of a charged particle. The widths of charged particle resonances at the ends of infinite-genus surfaces is not negligible and can be traced to the coupling with tachyons.https://www.mdpi.com/2624-960X/7/2/27resonancesMandelstam planecuspsideal boundarytachyon condensationcharged particle widths |
| spellingShingle | Simon Davis Quantization on the Ideal Boundary and the Finite Widths of Resonances Quantum Reports resonances Mandelstam plane cusps ideal boundary tachyon condensation charged particle widths |
| title | Quantization on the Ideal Boundary and the Finite Widths of Resonances |
| title_full | Quantization on the Ideal Boundary and the Finite Widths of Resonances |
| title_fullStr | Quantization on the Ideal Boundary and the Finite Widths of Resonances |
| title_full_unstemmed | Quantization on the Ideal Boundary and the Finite Widths of Resonances |
| title_short | Quantization on the Ideal Boundary and the Finite Widths of Resonances |
| title_sort | quantization on the ideal boundary and the finite widths of resonances |
| topic | resonances Mandelstam plane cusps ideal boundary tachyon condensation charged particle widths |
| url | https://www.mdpi.com/2624-960X/7/2/27 |
| work_keys_str_mv | AT simondavis quantizationontheidealboundaryandthefinitewidthsofresonances |