Title: Deformation Quantization of Nambu Mechanics Show Chinese title

Title: Nambu力学的形变量子化

Abstract: Phase Space is the framework best suited for quantizing superintegrable systems--systems with more conserved quantities than degrees of freedom. In this quantization method, the symmetry algebras of the hamiltonian invariants are preserved most naturally, as illustrated on nonlinear $\sigma$-models, specifically for Chiral Models and de Sitter $N$-spheres. Classically, the dynamics of superintegrable models such as these is automatically also described by Nambu Brackets involving the extra symmetry invariants of them. The phase-space quantization worked out then leads to the quantization of the corresponding Nambu Brackets, validating Nambu's original proposal, despite excessive fears of inconsistency which have arisen over the years. This is a pedagogical talk based on hep-th/0205063 and hep-th/0212267, stressing points of interpretation and care needed in appreciating the consistency of Quantum Nambu Brackets in phase space. For a parallel discussion in Hilbert space, see T Curtright's contribution in these Proceedings. Show Chinese abstract

Abstract: 相空间是用于量化超可积系统——即具有比自由度更多的守恒量的系统——的最佳框架。 在这种量化方法中，哈密顿不变量的对称代数最自然地被保留，如在非线性$\sigma$-模型上的说明，特别是对于手征模型和德西特$N$-球面。 经典上，这些超可积模型的动力学也自动由包含它们额外对称不变量的纳姆布括号来描述。 然后进行的相空间量化导致了相应纳姆布括号的量化，尽管多年来出现了过多的不一致担忧，但验证了纳姆布最初的提议。 这是一次教学性的演讲，基于 hep-th/0205063 和 hep-th/0212267，强调了理解相空间中量子纳姆布括号一致性的解释要点和需要注意的地方。 关于希尔伯特空间中的平行讨论，请参见 T Curtright 在本论文集中的贡献。