论 $C^{\infty}(\mathbb R^d)$ 的量子化
On the quantization of $C^{\infty}(\mathbb R^d)$
AI总结：
本文证明基本万有形变公式，刻画 $C^{\infty}(\mathbf R^d)$ 上初级障碍消失的无穷小形变与 Poisson 结构，并指出三维情形的特殊性质及其宇宙学启示。
摘要：
本文证明了基本万有形变公式，并应用它表明：编码 Heisenberg 不确定性原理的 Weyl 代数是多项式环的有效形变，而且不确定性对于稳定性是必要的。形变问题可以具有相伴的模群，文中给出了一个代数例子。$C^{\infty}(\mathbf R^d)$ 上的 Poisson 结构曾被 Kontsevich 证明为可积成完整形变的无穷小形变；本文则表明，它们正是 $C^{\infty}(\mathbf R^d)$ 的那些初级障碍消失的无穷小形变的反对称形式。在三维中，此类无穷小的任意光滑倍数仍具有消失的初级障碍。这一异常性质暗示，在我们的宇宙中，像大爆炸这样的巨大扰动可以被限制在任意小的时间区间内，并且几乎完全被限制在任意小的空间区域内。
英文摘要：
The Basic Universal Deformation Formula is proven and applied to show that Weyl algebras, which encode Heisenberg's uncertainty principle, are effective deformations of polynomial rings, and that uncertainty is necessary for stability. Deformation problems may have associated modular groups an algebraic example of which is given. Poisson structures on $C^{\infty}(\mathbf R^d)$, shown by Kontsevich to be infinitesimal deformations integrable to full deformations, here are shown to be the skew forms of those infinitesimal deformations of $C^{\infty}(\mathbf R^d)$ with vanishing primary obstructions. In dimension 3 any smooth multiple of such an infinitesimal again has vanishing primary obstruction. This exceptional property suggests that in our universe a large disturbance like the Big Bang can be confined to an arbitrarily small interval in time and almost completely confined to an arbitrarily small region in space.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
