Lambert-W Solves the Noncommutative $$\varPhi ^4$$-Model
| Autor: | Raimar Wulkenhaar, Erik Panzer |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
High Energy Physics - Theory
Pure mathematics Series (mathematics) Mathematics - Complex Variables 010102 general mathematics Holomorphic function Statistical and Nonlinear Physics Function (mathematics) 01 natural sciences Noncommutative geometry symbols.namesake Lambert W function 0103 physical sciences symbols 010307 mathematical physics Boundary value problem Hilbert transform 0101 mathematics Resummation 45G05 30E25 30E20 30B40 40E99 Mathematical Physics Mathematics |
| Zdroj: | Communications in Mathematical Physics. 374:1935-1961 |
| ISSN: | 1432-0916 0010-3616 |
| DOI: | 10.1007/s00220-019-03592-4 |
| Popis: | The closed Dyson-Schwinger equation for the 2-point function of the noncommutative $\lambda \phi^4_2$-model is rearranged into the boundary value problem for a sectionally holomorphic function in two variables. We prove an exact formula for a solution in terms of Lambert's $W$-function. This solution is holomorphic in $\lambda$ inside a domain which contains $(-1/\log 4,\infty)$. Our methods include the Hilbert transform, perturbation series and Lagrange-B\"urmann resummation. Comment: LaTeX, 28 pages, 2 figures. v2: main conjecture in v1 is now a theorem |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink