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A Noether-enhanced Legendre transformation from Lagrange densities toenergy-momentum tensors is developed into an alternative framework forformulating classical field equations. This approach offers direct access tothe Hamiltonian while keeping manifest Lorentz covariance in the formulation ofrelativistic field theories. The field equations are obtained by imposing avanishing divergence of the energy-momentum tensor (in a suitably structuredform). The proposed framework is ideally suited for coupling subsystems becausetheir interaction can be expressed as an exchange of energy and momentum. Evenhigher derivative theories and dissipative systems can be treated. A mostpromising application is the formulation of alternative theories of gravity.The proposed framework is illustrated for Yang-Mills theories, for which itoffers a covariant canonical quantization scheme.

An Alternative to the Lagrangian and Hamiltonian Formulations of Relativistic Field Theories Based on the Energy-Momentum Tensor