1993/07/03 by Dolan, Brian P.
#FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.hep-th/9307024
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 β-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 β-functions.