Author:
Buring Ricardo,Kiselev Arthemy V
Abstract
Abstract
The formula ⋆ mod ō(ħ
k
) of Kontsevich’s star-product with harmonic propagators was known in full at ħ
k⩾6 since 2018 for generic Poisson brackets, and since 2022 also at k = 7 for affine brackets. We discover that the mechanism of associativity for the star-product up to ō(ħ
6) is different from the mechanism at order 7 for both the full star-product and the affine star-product. Namely, at lower orders the needed consequences of the Jacobi identity are immediately obtained from the associator mod ō(ħ
6), whereas at order ħ
7 and higher, some of the necessary differential consequences are reached from the Kontsevich graphs in the associator in strictly more than one step.
Subject
Computer Science Applications,History,Education
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