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arXiv · 1807.02945

Lambert-W solves the noncommutative $\Phi^4$-model

Erik Panzer·Raimar Wulkenhaar
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Abstract

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.

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Erik Panzer, Raimar Wulkenhaar. 2018-07-09. Lambert-W solves the noncommutative $\Phi^4$-model. https://doi.org/10.1007/s00220-019-03592-4

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