1306.5840 (R. Flores et al.)

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

R. Flores, J. A. Nieto, J. Tellez, E. A. Leon, E. R. Estrada

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.

View original: http://arxiv.org/abs/1306.5840