Abstract
From ’t Hooft’s argument, one expects that the analyticity domain of an asymptotically free quantum field theory is horn shaped. In the usual Borel summation, the function is obtained through a Laplace transform and thus has a much larger analyticity domain. However, if the summation process goes through the process called acceleration by Écalle, one obtains such a horn-shaped analyticity domain. We therefore argue that acceleration, which allows to go beyond standard Borel summation, must be an integral part of the toolkit for the study of exactly renormalisable quantum field theories. We sketch how this procedure is working and what are its consequences.
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Notes
This means that the defining power series is convergent in some neighborhood of 0 and that the holomorphic function thus defined can be continued to the whole complex plane apart from a discrete set of singularities.
In principle, other round of accelerations could be necessary before the final Laplace transform, but once again, we do not aim at describing the most general procedure.
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Bellon, M.P., Clavier, P.J. Analyticity domain of a quantum field theory and accelero-summation. Lett Math Phys 109, 2003–2011 (2019). https://doi.org/10.1007/s11005-019-01172-0
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DOI: https://doi.org/10.1007/s11005-019-01172-0