Differential formulation of the dynamic renormalisation group in the large-n limit

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Abstract
A differential formulation of the dynamic renormalisation group in the large-n limit is presented for the time-dependent generalisation of the n-vector classical model with purely relaxational dynamics for both conserved and non-conserved order parameter. A discussion of the dynamical properties with the same steps used in the traditional perturbative approaches is made in terms of which known and new explicit results are obtained. Furthermore, a mechanical analogy is introduced which may give new information about the structure of the dynamic renormalisation group in the large-n limit. This relies on the possibility of using the well known geometrical and mathematical techniques from the Hamilton-Jacobi theory for classical mechanics.

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