The Casimir operator of SO(1,2) and the Pöschl-Teller potential: an AdS approach
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| Format: | Artículo científico |
| Language: | en |
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Sociedad Mexicana de Física A.C.
2005
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| author | R. da Rocha |
| author_facet | R. da Rocha |
| contents | The Casimir operator of SO(1,2) and the Pöschl-Teller potential: an AdS approach R. da Rocha E. Capelas de Oliveira Física, Astronomía y Matemáticas anti Pöschl Casimir Cartan form Teller potential We present and discuss some features of the anti-de Sitter spacetime, that is jointly with de Sitter and Minkowski is only, the unique maximalisotropic manifold. Among all possible lorentzian manifolds, we restrict our attention to the anti-de Sitter (AdS) spacetime, with metricdiag(1,¡1;¡1). We start by presenting the conformal time metric on AdS and we then show how we can obtain the Schrödinger formalism[1]. The Lie algebra so(1,2) is introduced and used to construct spin and ladder operators. After presenting the unitary representations,the AdS(1,2) spacetime is suitably parametrized and a representation of SO(1,2) is obtained, from which the Schrödinger equation withPöschl-Teller potential is immediately deduced. Finally, we discuss some relations between the relativistic harmonic oscillator and theKlein-Gordon equation, using the AdS(1,2) static frame. Possible applications of the presented formalism are provided. 2005 artículo científico 0035-001X https://www.redalyc.org/articulo.oa?id=57063701 en http://www.redalyc.org/revista.oa?id=570 Revista Mexicana de Física application/pdf Sociedad Mexicana de Física A.C. Revista Mexicana de Física (México) Num.1 Vol.51 |
| format | Artículo científico |
| id | redalyc_57063701 |
| institution | Redalyc |
| language | en |
| publishDate | 2005 |
| publisher | Sociedad Mexicana de Física A.C. |
| spellingShingle | The Casimir operator of SO(1,2) and the Pöschl-Teller potential: an AdS approach R. da Rocha Física, Astronomía y Matemáticas anti Pöschl Casimir Cartan form Teller potential The Casimir operator of SO(1,2) and the Pöschl-Teller potential: an AdS approach R. da Rocha E. Capelas de Oliveira Física, Astronomía y Matemáticas anti Pöschl Casimir Cartan form Teller potential We present and discuss some features of the anti-de Sitter spacetime, that is jointly with de Sitter and Minkowski is only, the unique maximalisotropic manifold. Among all possible lorentzian manifolds, we restrict our attention to the anti-de Sitter (AdS) spacetime, with metricdiag(1,¡1;¡1). We start by presenting the conformal time metric on AdS and we then show how we can obtain the Schrödinger formalism[1]. The Lie algebra so(1,2) is introduced and used to construct spin and ladder operators. After presenting the unitary representations,the AdS(1,2) spacetime is suitably parametrized and a representation of SO(1,2) is obtained, from which the Schrödinger equation withPöschl-Teller potential is immediately deduced. Finally, we discuss some relations between the relativistic harmonic oscillator and theKlein-Gordon equation, using the AdS(1,2) static frame. Possible applications of the presented formalism are provided. 2005 artículo científico 0035-001X https://www.redalyc.org/articulo.oa?id=57063701 en http://www.redalyc.org/revista.oa?id=570 Revista Mexicana de Física application/pdf Sociedad Mexicana de Física A.C. Revista Mexicana de Física (México) Num.1 Vol.51 |
| title | The Casimir operator of SO(1,2) and the Pöschl-Teller potential: an AdS approach |
| topic | Física, Astronomía y Matemáticas anti Pöschl Casimir Cartan form Teller potential |
| url | https://www.redalyc.org/articulo.oa?id=57063701 |