Abstract

FLORES, R. et al. SL(2,R)-geometric phase space and (2+2)-dimensions. Rev. mex. fis. [online]. 2013, vol.59, n.4, pp.352-358. ISSN 0035-001X.

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.

Keywords : Symplectic geometry; constrained Hamiltonian systems; two time physics.

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