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Dirac Oscillator in a Galilean Covariant Non-commutative Space |
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| Authors: | G. R. de Melo M. de Montigny P. J. Pompeia E. S. Santos |
| Affiliation: | 1. Núcleo Interdisciplinar em Ciência, Engenharia e Tecnologia Centro de Ciências Exatas e Tecnológicas, Universidade Federal do Rec?ncavo da Bahia, Campus Universitário de Cruz das Almas, 44380-000, Cruz das Almas, Bahia, Brazil 2. Theoretical Physics Institute, University of Alberta, Edmonton, Alberta, Canada, T6G 2E1 3. Faculté Saint-Jean, University of Alberta, Edmonton, Alberta, Canada, T6C 4G9 4. Departamento de Ciência e Tecnologia Aeroespacial, Instituto de Fomento e Coordena??o Industrial, Pra?a Marechal Eduardo Gomes, 50, Vila das Acácias, CEP 12.228-901, S?o José dos Campos, SP, Brazil 5. Instituto de Física, Universidade Federal da Bahia, 40210-340, Salvador, Bahia, Brazil |
| Abstract: | We study the Galilean Dirac oscillator in a non-commutative situation, with space-space and momentum-momentum non-commutativity. The wave equation is obtained via a ‘Galilean covariant’ approach, which consists in projecting the covariant equations from a (4,1)-dimensional manifold with light-cone coordinates, to a (3,1)-dimensional Galilean space-time. We obtain the exact wave functions and their energy levels for the plane and discuss the effects of non-commutativity. |
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