Working paper

### Lambert-W solves the noncommutative $Φ^4$-model

Abstract:

We show that the closed Dyson-Schwinger equation for the 2-point function of the noncommutative λϕ42-model can be rearranged into the boundary value problem Ψ(a+,b+)Ψ(a−,b−)=Ψ(a+,b−)Ψ(a−,b+) for a sectionally holomorphic function Ψ. This expresses the 2-point function as Hilbert transform of an angle function which itself satisfies a highly non-linear integral equation. A solution of that equation as formal power series in λ shows a surprisingly simple structure. The solution to 10th order is...

Publication status:
Not published
Peer review status:
Not peer reviewed

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### Authors

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
All Souls College
Role:
Author
ORCID:
0000-0002-9897-5812
Publication date:
2018-07-09
Source identifiers:
866178
Keywords:
Pubs id:
pubs:866178
UUID:
uuid:972224ac-f3b2-42a9-a4bf-8fe4deedacd6
Local pid:
pubs:866178
Deposit date:
2018-08-10