多自由度系统的Nambu动力学及其非正则Hamilton表示
Nambu dynamics and its noncanonical Hamiltonian representation in many degrees of freedom systems
摘要：
Nambu动力学是一种广义的两个以上变量的Hamilton动力学，其时间演化由Nambu括号给出，Nambu括号是正则泊松括号的推广。通过用Nambu括号定义非正则泊松括号，Nambu动力学总是可以用非正则哈密顿动力学的形式表示。为了使时间演化是一致的，Nambu括号必须满足基本恒等式，而非正则泊松括号必须满足雅可比恒等式。然而，在许多自由度系统中，众所周知，基本恒等式不成立。在本文中，我们表明，即使违反基本恒等式，相应的非正则哈密顿动力学的雅可比恒等式可以保持。作为一个例子，我们评估这些身份的半经典系统的两个耦合振子。
英文摘要：
Nambu dynamics is a generalized Hamiltonian dynamics of more than two variables, whose time evolutions are given by the Nambu bracket, a generalization of the canonical Poisson bracket. Nambu dynamics can always be represented in the form of noncanonical Hamiltonian dynamics by defining the noncanonical Poisson bracket by means of the Nambu bracket. For the time evolution to be consistent, the Nambu bracket must satisfy the fundamental identity, while the noncanonical Poisson bracket must satisfy the Jacobi identity. However, in many degrees of freedom systems, it is well known that the fundamental identity does not hold. In the present paper we show that, even if the fundamental identity is violated, the Jacobi identity for the corresponding noncanonical Hamiltonian dynamics could hold. As an example, we evaluate these identities for a semiclassical system of two coupled oscillators.
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