Quantum dynamics of the effective field theory of the Calogero-Sutherland model
We consider the known effective field theory of the Calogero-Sutherland model in the thermodynamic limit of large number of particles, obtained from the standard procedure in conformal field theory: the Hilbert space is constructed a priori in terms of irreducible representations of the symmetry alg...
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| Format: | Article |
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Elsevier
2025-03-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321325000355 |
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| author | Federico L. Bottesi Guillermo R. Zemba |
| author_facet | Federico L. Bottesi Guillermo R. Zemba |
| author_sort | Federico L. Bottesi |
| collection | DOAJ |
| description | We consider the known effective field theory of the Calogero-Sutherland model in the thermodynamic limit of large number of particles, obtained from the standard procedure in conformal field theory: the Hilbert space is constructed a priori in terms of irreducible representations of the symmetry algebra, and not by diagonalization of the hamiltonian, which is given in terms of fields that carry representations of the W1+∞ algebra (representing the incompressibility of the Fermi sea). Nevertheless, the role of the effective hamiltonian of the theory is to establish a specific dynamics, which deserves further consideration. We show that the time evolution of the (chiral or antichiral) density field is given by the quantum Benjamin-Ono equation, in agreement with previous results obtained from the alternative description of the continuous limit of the model, based on quantum hydrodynamics. In this study, all calculations are performed at the quantum operator level, without making any assumption on the semiclassical limit of the fields and their equations of motion. This result may be considered as a reliable indication of the equivalence between the quantum field theoretic and quantum hydrodynamical formulations of the effective theories of the model. A one-dimensional quantum compressible fluid that includes both chiralities is the physical picture that emerges for the continuous limit of the Calogero-Sutherland model. |
| format | Article |
| id | doaj-art-752198525ec34cf7b2479679795737a3 |
| institution | Kabale University |
| issn | 0550-3213 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj-art-752198525ec34cf7b2479679795737a32025-02-11T04:33:31ZengElsevierNuclear Physics B0550-32132025-03-011012116825Quantum dynamics of the effective field theory of the Calogero-Sutherland modelFederico L. Bottesi0Guillermo R. Zemba1Facultad de Ingeniería, Universidad de Buenos Aires, Av. Paseo Colón 850, (C1063ACL) Buenos Aires, ArgentinaDepartamento de Física Teórica, GIyA, Laboratorio Tandar, Comisión Nacional de Energía Atómica, Av. Libertador 8250, (C1429BNP) Buenos Aires, Argentina; Facultad de Ingeniería y Ciencias Agrarias, Pontificia Universidad Católica Argentina, Av. Alicia Moreau de Justo 1500, (C1107AAZ) Buenos Aires, Argentina; Corresponding author.We consider the known effective field theory of the Calogero-Sutherland model in the thermodynamic limit of large number of particles, obtained from the standard procedure in conformal field theory: the Hilbert space is constructed a priori in terms of irreducible representations of the symmetry algebra, and not by diagonalization of the hamiltonian, which is given in terms of fields that carry representations of the W1+∞ algebra (representing the incompressibility of the Fermi sea). Nevertheless, the role of the effective hamiltonian of the theory is to establish a specific dynamics, which deserves further consideration. We show that the time evolution of the (chiral or antichiral) density field is given by the quantum Benjamin-Ono equation, in agreement with previous results obtained from the alternative description of the continuous limit of the model, based on quantum hydrodynamics. In this study, all calculations are performed at the quantum operator level, without making any assumption on the semiclassical limit of the fields and their equations of motion. This result may be considered as a reliable indication of the equivalence between the quantum field theoretic and quantum hydrodynamical formulations of the effective theories of the model. A one-dimensional quantum compressible fluid that includes both chiralities is the physical picture that emerges for the continuous limit of the Calogero-Sutherland model.http://www.sciencedirect.com/science/article/pii/S0550321325000355 |
| spellingShingle | Federico L. Bottesi Guillermo R. Zemba Quantum dynamics of the effective field theory of the Calogero-Sutherland model Nuclear Physics B |
| title | Quantum dynamics of the effective field theory of the Calogero-Sutherland model |
| title_full | Quantum dynamics of the effective field theory of the Calogero-Sutherland model |
| title_fullStr | Quantum dynamics of the effective field theory of the Calogero-Sutherland model |
| title_full_unstemmed | Quantum dynamics of the effective field theory of the Calogero-Sutherland model |
| title_short | Quantum dynamics of the effective field theory of the Calogero-Sutherland model |
| title_sort | quantum dynamics of the effective field theory of the calogero sutherland model |
| url | http://www.sciencedirect.com/science/article/pii/S0550321325000355 |
| work_keys_str_mv | AT federicolbottesi quantumdynamicsoftheeffectivefieldtheoryofthecalogerosutherlandmodel AT guillermorzemba quantumdynamicsoftheeffectivefieldtheoryofthecalogerosutherlandmodel |