Exact conservation laws of the gradient expanded Kadanoff-Baym equations

It is shown that the Kadanoff-Baym equations at consistent first-order grad ient approximation reveal exact rather than approximate conservation laws r elated to global symmetries of the system. The conserved currents and energ y-momentum tensor coincide with corresponding Noether quantities in the loc al approximation. These exact conservations are valid, provided a cl) deriv able approximation is used to describe die system, and possible memory effe cts in the collision term are also consistently evaluated up to first-order gradients. (C) 2001 Academic Press.