Gauge group,degeneration, and degrees of freedom in the ECSK theory of gravity. I. The symplectic structure of the ECSK theory

This paper is the first of a two-article series in which the connections between the gauge group, degeneration, and degrees of freedom in the ECSK theory coupled to an arbitrary tensor field are discussed. In this paper a multisymplectic formulation of the ECSK theory is presented and the symplectic 2-form, which plays a leading role in our considerations, is found.