Convergence of derivative expansions of the renormalization group | Zendy

Tim R. Morris | Zendy; John F. Tighe | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

Convergence of derivative expansions of the renormalization group

Author(s) -

Tim R. Morris,

John F. Tighe

Publication year - 1999

Publication title -

journal of high energy physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.998

H-Index - 261

eISSN - 1126-6708

pISSN - 1029-8479

DOI - 10.1088/1126-6708/1999/08/007

Subject(s) - cutoff , mathematics , renormalization group , mathematical analysis , radius of convergence , exponential function , momentum (technical analysis) , mathematical physics , scalar (mathematics) , derivative (finance) , convergence (economics) , asymptotic expansion , physics , quantum mechanics , power series , geometry , finance , economics , financial economics , economic growth

We investigate the convergence of the derivative expansion of the exactrenormalization group, by using it to compute the beta function of scalar fieldtheory. We show that the derivative expansion of the Polchinski flow equationconverges at one loop for certain fast falling smooth cutoffs. The derivativeexpansion of the Legendre flow equation trivially converges at one loop, butalso 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 thatthe two loop contributions to certain higher derivative operators (not involvedin beta) have divergent momentum-scale expansions for sharp cutoff, but thesmooth exponential cutoff gives convergent derivative expansions for all suchoperators with any number of derivatives.Comment: Latex inc axodraw. 20 page

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research