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

R. Flores^a, J. A. Nieto^b,a, J. Tellez^a, E. A. Leon^b, and E. R. Estrada^c

^a Departamento de Investigación en Física de la Universidad de Sonora, 83000, Hermosillo Sonora, México. e-mail: rflorese@gauss.mat.uson.mx; jtellez@cajeme.cifus.uson.mx.

^b Facultad de Ciencias Físico-Matemáticas de la Universidad Autónoma de Sinaloa, 80010, Culiacán Sinaloa, México. e-mail: niet@uas.edu.mx; janieto1@asu.edu; ealeon@uas.edu.mx.

^c Instituto Tecnológico Superior de Eldorado, Eldorado, Sinaloa, México. e-mail: profe.emmanuel@gmail.com.

Received 23 November 2012
Accepted 19 April 2013

Abstract

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.

PACS: 04.20.Gz; 04.60.-Ds; 11.30.Ly

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Acknowledgments

This work was partially supported by PROFAPI-UAS 2009.

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