The Renormalisation Group Equation As An Equation For Lie Transport Of Amplitudes

Details The Renormalisation Group Equation As An Equation For Lie Transport Of Amplitudes The Renormalisation Group Equation As An Equation For Lie Transport Of Amplitudes

1993-07-03

arxiv.org/abs/hep-th/9307024v1

Physics

High Energy Physics

High Energy Physics - Theory

8 pages Typeset in PlainTeX, C Version 3.141

Scientific paper

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.

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