SL(2,R)-geometric phase space and (2+2)-dimensions

• Autores: R. Flores, J. A. Nieto, J. Tellez, E.A. León, E.R. Estrada
• Localización: Revista Mexicana de Física, ISSN-e 0035-001X, Vol. 59, Nº. 4, 2013, págs. 352-358
• Idioma: inglés
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• Resumen

  • We propose an alternative geometric mathematical structure for arbitrary phase space. The main guide in our approach is the hidden SL(2,R)-symmetry which acts on the phase space changing coordinates by momenta and vice versa. We show that the SL(2,R)-symmetry is implicit in any simplectic structure. We also prove that in any sensible physical theory based on the SL(2,R)-symmetry the signature of the flat target "spacetime" must be associated with either one-time and one-space or at least two-time and two-space coordinates. We discuss the consequences as well as possible applications of our approach on different physical scenarios.