Energy-Momentum Conservation Laws in Affine-Metric Gravitation Theory

The Lagrangian formulation of field theory does not provide any universal energy-momentum conservation law in order to analize that in gravitation theory. In Lagrangian field theory, we get different identities involving different stress energy-momentum tensors which however are not conserved, otherwise in the covariant multimomentum Hamiltonian formalism. In the framework of this formalism, we have the fundamental identity whose restriction to a constraint space can be treated the energy-momentum transformation law. This identity remains true also for gravity. Thus, the tools are at hand to investigate the energy-momentum conservation laws in gravitation theory. The key point consists in the feature of a metric gravitational field whose canonical momenta on the constraint space are equal to zero.