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A novel reduction procedure for covariant classical field theories,reflecting the generalized symplectic reduction theory of Hamiltonian systems,is presented. The departure point of this reduction procedure consists in thechoice of a submanifold of the manifold of solutions of the equationsdescribing a field theory. Then, the covariance of the geometrical objectsinvolved, will allow to define equations of motion on a reduced space. Thecomputation of the canonical geometrical structure is performed neatly by usingthe geometrical framework provided by the multisymplectic description ofcovariant field theories. The procedure is illustrated by reducing theD'Alembert theory on a five-dimensional Minkowski space-time to a massiveKlein-Gordon theory in four dimensions and, more interestingly, to theSchr\"odinger equation in 3+1 dimensions.

Covariant reduction of classical Hamiltonian Field Theories: From D'Alembert to Klein-Gordon and Schr\"odinger