Noncommutative differential geometry via deformation quantization and quantum effects of gravity

Haoyuan Gao 高浩元  (Fudan University)

10:00-11:00, November 21, 2023   Science Building A503 & Tencent Meeting 774555390


The asymptotic expansion of Weyl quantization with respect to the Planck constant yields an associative but noncommutative formal product on the space of classical observables, called the Moyal-Weyl product. This is the simplest non-trivial example of deformation quantization. We introduce a noncommutative version of Riemannian geometry in the framework of Moyal-Weyl product. This enables us to propose the noncommutative Einstein field equations and study quantum effects of gravity. We will see the two noncommutative Ricci curvatures are equivalent in certain conditions, which hold automatically for quantum fluctuations given by an isometric embedding. We will also discuss renormalization of quantization of spherically symmetric metrics. This talk is based on the joint work with Xiao Zhang.

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