论文标题
NAMBU力学被视为Clebsch参数化泊松代数 - 朝着规范化和量化
Nambu mechanics viewed as a Clebsch parameterized Poisson algebra -- toward canonicalization and quantization
论文作者
论文摘要
在他的开创性论文中[物理学。 E Rev. E 7，2405（1973）]，Nambu提出了多个哈密顿系统的想法。所检查的明确示例等同于So（3）Lie-Poisson系统，该系统代表具有Casimir的非规范性汉密尔顿动力学； Casimir对应于Nambu配方的第二次哈密顿量。理想流体的涡流动力学虽然是无限的尺寸，但具有相似的结构，其中casimir是螺旋性。这些非规范的泊松代数是通过还原来得出的，即将相空间限制在规范相空间中嵌入的某些子曼群。我们可能会扭转减少范围，以使某些NAMBU动力学，即将Nambu动力学视为较大的规范泊松代数的子代数。然后，我们可以调用用于量化规范化系统的标准相应原理。在流体机械示例之后，可以说还要说“ clebsch参数化”的降低的倒数，即代表某些规范变量的非规范变量。
In his pioneering paper [Phys. Rev. E 7, 2405 (1973)], Nambu proposed the idea of multiple Hamiltonian systems. The explicit example examined there is equivalent to the so(3) Lie-Poisson system, which represents noncanonical Hamiltonian dynamics with a Casimir; the Casimir corresponds to the second Hamiltonian of Nambu's formulation. The vortex dynamics of ideal fluid, while it is infinite dimensional, has a similar structure, in which the Casimir is the helicity. These noncanonical Poisson algebras are derived by the reduction, i.e., restricting the phase space to some submanifold embedded in the canonical phase space. We may reverse the reduction to canonicalize some Nambu dynamics, i.e., view the Nambu dynamics as the subalgebra of a larger canonical Poisson algebra. Then, we can invoke the standard corresponding principle for quantizing the canonicalized system. The inverse of the reduction, i.e., representing the noncanonical variables by some canonical variables may be said "Clebsch parameterization" following the fluid mechanical example.
