Large N quantum time evolution beyond leading order - art. no. 125003

For quantum theories with a classical limit (which includes the large N lim its of typical field theories), we derive a hierarchy of evolution equation s for equal time correlators which systematically incorporate corrections t o the limiting classical evolution. Explicit expressions are given for next -to-lending order, and next-to-next-to-leading order time evolution. The la rge N limit of N-component vector models, and the usual semiclassical limit of point particle quantum mechanics are used as concrete examples. Our for mulation directly exploits the appropriate group structure which underlies the construction of suitable coherent states and generates the classical ph ase space. We discuss the growth of truncation error with time, and argue t hat truncations of the large-N evolution equations are generically expected to be useful only for times short compared to a "decoherence" time which s cales like N-1/2.