Large N Quantum Time Evolution Beyond Leading Order

Details Large N Quantum Time Evolution Beyond Leading Order Large N Quantum Time Evolution Beyond Leading Order

2000-06-29

arxiv.org/abs/hep-ph/0006333v1

Phys.Rev. D62 (2000) 125003

Physics

High Energy Physics

High Energy Physics - Phenomenology

36 pages, 2 eps figures, latex, uses revtex, epsfig, floats

Scientific paper

10.1103/PhysRevD.62.125003

For quantum theories with a classical limit (which includes the large N limits of typical field theories), we derive a hierarchy of evolution equations for equal time correlators which systematically incorporate corrections to the limiting classical evolution. Explicit expressions are given for next-to-leading order, and next-to-next-to-leading order time evolution. The large N limit of N-component vector models, and the usual semiclassical limit of point particle quantum mechanics are used as concrete examples. Our formulation directly exploits the appropriate group structure which underlies the construction of suitable coherent states and generates the classical phase space. We discuss the growth of truncation error with time, and argue that truncations of the large-N evolution equations are generically expected to be useful only for times short compared to a ``decoherence'' time which scales like N^{1/2}.

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