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The Faddeev-Jackiw symplectic formalism for constrained systems is applied toanalyze the dynamical content of a model describing two massive relativisticparticles with interaction, which can also be interpreted as a bigravity modelin one dimension. We systematically investigate the nature of the physicalconstraints, for which we also determine the zero-modes structure of thecorresponding symplectic matrix. After identifying the whole set ofconstraints, we find out the transformation laws for all the set of dynamicalvariables corresponding to gauge symmetries, encoded in the remainingzero-modes. In addition, we use an appropriate gauge-fixing procedure, theconformal gauge, to compute the quantization brackets (Faddeev-Jackiw brackets)and also obtain the number of physical degree of freedom. Finally, we arguethat this symplectic approach can be helpful for assessing physical constraintsand understanding the gauge structure of theories of interacting spin-2 fields.

Constrained dynamics of two interacting relativistic particles in the Faddeev-Jackiw symplectic framework