  It is shown that the renormalisation group (RG) equation can be viewed as an
equation for Lie transport of physical amplitudes along the integral curves
generated by the $\beta$-functions of a quantum field theory. The anomalous
dimensions arise from Lie transport of basis vectors on the space of couplings.
The RG equation can be interpreted as relating a particular diffeomorphism of
flat space-(time), that of dilations, to a diffeomorphism on the space of
couplings generated by the vector field associated with the $\beta$-functions.
