Borel convergence of the expansion around RG mass fixed point and the mass gap of asymptotically free models
✍ Scribed by J.-L. Kneur
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 403 KB
- Volume
- 121
- Category
- Article
- ISSN
- 0920-5632
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✦ Synopsis
We review a construction based on an expansion around a (mass) fixed point renormalization group solution, in asymptotically free models. It transmutes the usual perturbative expansion of certain physical quantities in such a way that the alternative expansion parameter l/F behaves like the ordinary coupling: F -ln(ti/A) in the perturbative regime r% > A, but like a power of A/& in the infrared regime T?Z 5 A (riz and A being the scale invariant mass and basic scale respectively). (Borel) convergence of the induced series can hold in a range of F corresponding to reach unambiguously the strong coupling infrared regime, near 7iz --t 0. We argue that certain nonperturbative quantities, such as the (pole) mass gap typically, can be thus obtained from a direct resummation of this alternative expansion (i.e. without adding intrinsically nonperturbative power-like contributions).