A simple geometric way is suggested to derive the Ward identities in the Chern-Simons theory, also known as quantum A- and C-polynomials for knots. In quasi-classical limit it is closely related to the well publicized augmentation theory and contact geometry. Quantization allows to present it in much simpler terms, what could make these techniques available to a broader audience. To avoid overloading of the presentation, only the case of the colored Jones polynomial for the trefoil knot is considered, though various generalizations are straightforward. Restriction to solely Jones polynomials (rather than full HOMFLY-PT) is related to a serious simplification, provided by the use of Kauffman calculus. Going beyond looks realistic, however it remains a problem, both challenging and promising.

中文翻译：

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关于量子 A 的 knot 多项式的几何基


在 Chern-Simons 理论中，建议使用一种简单的几何方法来推导出 Ward 恒等式，也称为结的量子 A 多项式和 C 多项式。在准经典极限中，它与广为人知的增强理论和接触几何密切相关。量化允许以更简单的术语呈现它，从而使这些技术可供更广泛的受众使用。为避免表示过载，仅考虑三叶草结的彩色 Jones 多项式的情况，尽管各种泛化都很简单。仅限于 Jones 多项式（而不是完整的 HOMFLY-PT）与使用 Kauffman 微积分提供的严重简化有关。超越似乎很现实，但它仍然是一个问题，既具有挑战性又有希望。