On the origin of the correspondence between classical and quantum integrable theories
If we start from certain functional relations as definition of a quantum integrable theory, then we can derive from them a linear integral equation. It can be extended, by introducing dynamical variables, to become an equation with the form of Marchenko's. Then, we derive from the latter a clas...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-03-01
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| Series: | Physics Letters B |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0370269323000400 |
| _version_ | 1797905348495933440 |
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| author | Davide Fioravanti Marco Rossi |
| author_facet | Davide Fioravanti Marco Rossi |
| author_sort | Davide Fioravanti |
| collection | DOAJ |
| description | If we start from certain functional relations as definition of a quantum integrable theory, then we can derive from them a linear integral equation. It can be extended, by introducing dynamical variables, to become an equation with the form of Marchenko's. Then, we derive from the latter a classical (differential) Lax pair. We exemplify our method by focusing on the massive version of the ODE/IM (Ordinary Differential Equations/Integrable Models) correspondence from Quantum sine-Gordon (sG) with many moduli/masses to the classical sinh-Gordon (shG) equation, so describing, in a particular case, some super-symmetric gauge theories and the AdS3 strong coupling scattering amplitudes/Wilson loops. Yet, we present it in a way which reveals its generality of application. In fact, we give some hints on how it works for spin chains. |
| first_indexed | 2024-04-10T10:03:53Z |
| format | Article |
| id | doaj.art-b567508c59c84ddebf5225cebca02c3a |
| institution | Directory Open Access Journal |
| issn | 0370-2693 |
| language | English |
| last_indexed | 2024-04-10T10:03:53Z |
| publishDate | 2023-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Physics Letters B |
| spelling | doaj.art-b567508c59c84ddebf5225cebca02c3a2023-02-16T04:17:40ZengElsevierPhysics Letters B0370-26932023-03-01838137706On the origin of the correspondence between classical and quantum integrable theoriesDavide Fioravanti0Marco Rossi1Sezione INFN di Bologna, Dipartimento di Fisica e Astronomia, Università di Bologna, Via Irnerio 46, 40126 Bologna, Italy; Corresponding author.Dipartimento di Fisica dell'Università della Calabria and INFN, Gruppo collegato di Cosenza, Arcavacata di Rende, 87036 Cosenza, ItalyIf we start from certain functional relations as definition of a quantum integrable theory, then we can derive from them a linear integral equation. It can be extended, by introducing dynamical variables, to become an equation with the form of Marchenko's. Then, we derive from the latter a classical (differential) Lax pair. We exemplify our method by focusing on the massive version of the ODE/IM (Ordinary Differential Equations/Integrable Models) correspondence from Quantum sine-Gordon (sG) with many moduli/masses to the classical sinh-Gordon (shG) equation, so describing, in a particular case, some super-symmetric gauge theories and the AdS3 strong coupling scattering amplitudes/Wilson loops. Yet, we present it in a way which reveals its generality of application. In fact, we give some hints on how it works for spin chains.http://www.sciencedirect.com/science/article/pii/S0370269323000400Integrable field theoriesODE/IM correspondenceBethe ansatzMarchenko equationSchrödinger equation |
| spellingShingle | Davide Fioravanti Marco Rossi On the origin of the correspondence between classical and quantum integrable theories Physics Letters B Integrable field theories ODE/IM correspondence Bethe ansatz Marchenko equation Schrödinger equation |
| title | On the origin of the correspondence between classical and quantum integrable theories |
| title_full | On the origin of the correspondence between classical and quantum integrable theories |
| title_fullStr | On the origin of the correspondence between classical and quantum integrable theories |
| title_full_unstemmed | On the origin of the correspondence between classical and quantum integrable theories |
| title_short | On the origin of the correspondence between classical and quantum integrable theories |
| title_sort | on the origin of the correspondence between classical and quantum integrable theories |
| topic | Integrable field theories ODE/IM correspondence Bethe ansatz Marchenko equation Schrödinger equation |
| url | http://www.sciencedirect.com/science/article/pii/S0370269323000400 |
| work_keys_str_mv | AT davidefioravanti ontheoriginofthecorrespondencebetweenclassicalandquantumintegrabletheories AT marcorossi ontheoriginofthecorrespondencebetweenclassicalandquantumintegrabletheories |