Symplectic geometry of the convariant phase space

Abstract

Develops a formalism for a covariant treatment of the phase space of field theories. Within that formalism, an expression for the symplectic form of a general Lagrangian field theory is presented. As examples, the author derives the symplectic forms for general relativity and for the Green-Schwarz covariant superstring action. Finally, an extension of the covariant phase space formalism to theories in superspace is given.