Abstract
It is shown that the Kadanoff-Baym equations at consistent first-order gradient approximation reveal exact rather than approximate conservation laws related to global symmetries of the system. The conserved currents and energy-momentum tensor coincide with corresponding Noether quantities in the local approximation. These exact conservations are valid, provided a Phi-derivable approximation is used to describe the system, and possible memory effects in the collision term are also consistently evaluated up to first-order gradients.
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