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Dimensional renormalization in phi(3) theory: Ladders and rainbows
journal contribution
posted on 2023-05-16, 10:27 authored by Robert DelbourgoRobert Delbourgo, David ElliottDavid Elliott, McAnally, DThe sum of all the ladder and rainbow diagrams in φ3 theory near six dimensions leads to self-consistent higher order differential equations in coordinate space which are not particularly simple for arbitrary dimension D. We have now succeeded in solving these equations, expressing the results in terms of generalized hyper-geometric functions; the expansion and representation of these functions can then be used to prove the absence of renormalization factors which are transcendental for this theory and this topology to all orders in perturbation theory. The correct anomalous scaling dimensions of the Green functions are also obtained in the sixdimensional limit.
History
Publication title
Physical Review DVolume
55Issue
8Pagination
5230-5233ISSN
0556-2821Department/School
School of Natural SciencesPublisher
The American Physical SocietyPlace of publication
Woodbury, New York, USARepository Status
- Restricted