no. 5
On the Moyal Star Product of Resurgent Series
[Sur le star produit de Moyal des séries résurgentes]
Li, Yong1 ; Sauzin, David2 ; Sun, Shanzhong3
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)
Annales de l'Institut Fourier, Tome 73 (2023) no. 5, pp. 1987-2027.

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 iℏ à coefficients dans ℂ{x 1 ,...,x d }), dont nous montrons qu’il est stable par star-produit de Moyal.

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 iℏ with coefficients in ℂ{x 1 ,...,x d }), which we show is stable under Moyal star product.

Reçu le :
Révisé le :
Accepté le :
Publié le :
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)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Li, Yong; Sauzin, David; Sun, Shanzhong. On the Moyal Star Product of Resurgent Series. Annales de l'Institut Fourier, Tome 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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