Geodesic Renormalisation Group Flow
Brian P. Dolan
Abstract
It is shown that the renormalisation group flow in coupling constant space can be interpreted in terms of a dynamical equation for the couplings analogous to viscous fluid flow under the action of a potential. For free scalar field theory the flow is geodesic in two dimensions, while for D ≠ 2 it is only geodesic in certain limits, e.g. for vanishing external source. For the 1-D Ising model the renormalisation flow is geodesic when the external magnetic field vanishes.
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