On the Moyal Star Product of Resurgent Series
Annales de l'Institut Fourier, Volume 73 (2023) no. 5, pp. 1987-2027.

We analyze the Moyal star product in deformation quantization from the resurgence theory perspective. By putting algebraic conditions on Borel transforms, one can define the space of “algebro-resurgent series” (a subspace of 1-Gevrey formal series in i with coefficients in {x 1 ,...,x d }), which we show is stable under Moyal star product.

Nous analysons le star produit de Moyal de la quantification par déformation sous l’angle de la théorie de la résurgence. En imposant des conditions algébriques sur les transformées de Borel, on peut définir l’espace des «  séries algébro-résurgentes  » (un sous-espace des séries formelles Gevrey-1 en l’indéterminée i à coefficients dans {x 1 ,...,x d }), dont nous montrons qu’il est stable par star-produit de Moyal.

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DOI: 10.5802/aif.3565
Classification: 53D55, 32Dxx
Keywords: Deformation quantization, Moyal product, Resurgence theory, Algebro-resurgent series, Hadamard product.
Mot clés : Quantification par déformation, produit de Moyal, théorie de la résurgence, séries algébro-résurgentes, produit de Hadamard.
Li, Yong 1; Sauzin, David 2; Sun, Shanzhong 3

1 Chern Institute of Mathematics and LPMC Nankai University Tianjin 300071 (China)
2 CNRS – Observatoire de Paris PSL Research University 75014 Paris (France)
3 Department of Mathematics and Academy for Multidisciplinary Studies Capital Normal University Beijing 100048 (China)
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Li, Yong; Sauzin, David; Sun, Shanzhong. On the Moyal Star Product of Resurgent Series. Annales de l'Institut Fourier, Volume 73 (2023) no. 5, pp. 1987-2027. doi : 10.5802/aif.3565. https://aif.centre-mersenne.org/articles/10.5802/aif.3565/

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