Symmetries of the Free Schrodinger Equation in the Non-Commutative Plane
We study all the symmetries of the free Schrodinger equation in the non-commutative plane. These symmetry transformations form an infinite-dimensional Weyl algebra that appears naturally from a two-dimensional Heisenberg algebra generated by Galilean boosts and momenta. These infinite high symmetrie...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2014 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/23380 |
| Acceso en línea: | https://hdl.handle.net/2117/23380 https://dx.doi.org/10.3842/SIGMA.2014.011 |
| Access Level: | acceso abierto |
| Palabra clave: | Schrödinger equation Algebra Mathematical physics non-commutative plane Schrodinger equation Schrodinger symmetries higher spin symmetries PHENOMENOLOGICAL LAGRANGIANS GALILEAN SYMMETRY FIELD-THEORY SCALE SPACE TERM Schrödinger, Equació de Àlgebra Física matemàtica Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals |
| Sumario: | We study all the symmetries of the free Schrodinger equation in the non-commutative plane. These symmetry transformations form an infinite-dimensional Weyl algebra that appears naturally from a two-dimensional Heisenberg algebra generated by Galilean boosts and momenta. These infinite high symmetries could be useful for constructing non-relativistic interacting higher spin theories. A finite-dimensional subalgebra is given by the Schrodinger algebra which, besides the Galilei generators, contains also the dilatation and the expansion. We consider the quantization of the symmetry generators in both the reduced and extended phase spaces, and discuss the relation between both approaches. |
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