Convergence of derivative expansions of the renormalization group

Details Convergence of derivative expansions of the renormalization group Convergence of derivative expansions of the renormalization group

1999-06-21

arxiv.org/abs/hep-th/9906166v1

JHEP 9908:007,1999

Physics

High Energy Physics

High Energy Physics - Theory

Latex inc axodraw. 20 pages

Scientific paper

10.1088/1126-6708/1999/08/007

We investigate the convergence of the derivative expansion of the exact renormalization group, by using it to compute the beta function of scalar field theory. We show that the derivative expansion of the Polchinski flow equation converges at one loop for certain fast falling smooth cutoffs. The derivative expansion of the Legendre flow equation trivially converges at one loop, but also at two loops: slowly with sharp cutoff (as a momentum-scale expansion), and rapidly in the case of a smooth exponential cutoff. Finally, we show that the two loop contributions to certain higher derivative operators (not involved in beta) have divergent momentum-scale expansions for sharp cutoff, but the smooth exponential cutoff gives convergent derivative expansions for all such operators with any number of derivatives.

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