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

Author(s): R. Flores | J. A. Nieto | J. Tellez | E. A. Leon | E. R. Estrada

Journal: Revista Mexicana de Física
ISSN 0035-001X

Volume: 59;
Issue: 4;
Start page: 352;
Date: 2013;
Original page

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 symplectic 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.
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