Symplectic realization of two interacting spin-two fields in three dimensions

A bstract We constructed a symplectic realization of the dynamic structure two interacting spin-two fields in three dimensions. significant simplification refers to treatment constraints: instead performing Hamiltonian analysis à la Dirac, we worked out method that only uses properties pre-symplectic two-form matrix and its corresponding zero-modes investigate nature constraints gauge theory. For instance, demonstrate contraction with potential gradient, yields explicit expressions for whole set on dynamics theory, including symmetrization condition an relationship between coupling cosmological constants. This way, further identify necessary conditions existence unique non-linear candidate partially massless using expression interaction parameters model. In case structure, transformation laws entire dynamical variables are more straightforwardly derived from remaining zero-modes; this sense, must be viewed as generators transformations. Thereafter, use appropriate gauge-fixing procedure, time gauge, compute both quantization brackets functional measure path integral associated our Finally, confirm three-dimensional bi-gravity has physical degrees freedom per space point. With above, provide new perspective better understanding theories fields, which does not require catalogued first- second-class ones Dirac’s standard method.