Potentials on the conformally compactified Minkowski spacetime and their application to quark deconfinement
We study a class of conformal metric deformations in the quasi-radial coordinate parameterizing the 3-sphere in the conformally compactified Minkowski spacetime S1 ×S3. Prior to reduction of the associated Laplace-Beltrami operators to a Schr¨odinger form, a corresponding class of exactly solvable p...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universidad Nacional de Educación a Distancia |
| Repositorio: | e-spacio. Repositorio Institucional de la UNED |
| Idioma: | inglés |
| OAI Identifier: | oai:e-spacio.uned.es:20.500.14468/25021 |
| Acceso en línea: | https://hdl.handle.net/20.500.14468/25021 |
| Access Level: | acceso abierto |
| Palabra clave: | 12 Matemáticas::1204 Geometría Conformal symmetry exactly and quasi-exactly solvable potentials quark confinement |
| Sumario: | We study a class of conformal metric deformations in the quasi-radial coordinate parameterizing the 3-sphere in the conformally compactified Minkowski spacetime S1 ×S3. Prior to reduction of the associated Laplace-Beltrami operators to a Schr¨odinger form, a corresponding class of exactly solvable potentials (each one containing a scalar and a gradient term) is found. In particular, the scalar piece of these potentials can be exactly or quasi-exactly solvable, and among them we find the finite range confining trigonometric potentials of P¨oschl-Teller, Scarf and Rosen-Morse. As an application of the results developed in the paper, the large compactification radius limit of the interaction described by some of these potentials is studied, and this regime is shown to be relevant to a quantum mechanical quark deconfinement mechanism. |
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