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Exact and approximate dynamics of the quantum mechanical<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mi>N</mml:mi><mml:mo>)</mml:mo><mml:mn /></mml:math>model
We study the dynamics of the quantum mechanical $O(N)$ model as a specific example to investigate the systematics of a $1/N$ expansion. The closed time path formalism melded with an expansion in $1/N$ is used to derive time evolution equations valid to order $1/N$ (next-to-leading order). The effective potential is …