论文标题
广义的几何换向器理论和量子几何括号及其用途
Generalized geometric commutator theory and quantum geometric bracket and its uses
论文作者
论文摘要
Inspired by the geometric bracket for the generalized covariant Hamilton system, we abstractly define a generalized geometric commutator $$\left[ a,b \right]={{\left[ a,b \right]}_{cr}}+G\left(s,a,b \right)$$ formally equipped with geomutator $G\left(s, a,b \ right）= a {{{\ left [s，b \ right]} _ {cr}} - b {{{\ left [s，a \ right]} _ {cr}} $根据结构函数$ s $定义的定义，该函数$ s $ s $与Spacetime或流形的结构相关，以修改经典代表的结构\ right]} _ {cr}} =任何代数的任何元素$ a $和$ b $的ab-ba $。 然后，我们使用广义的几何换向器来定义量子协变量托架支架，该托架托架与地图泊松托架的概括性定义的量子几何支架相关。协变性动力学包括基于量子几何括号的海森堡方程和G-Dynemics的自然扩展，包括量子几何括号，同时诱发了几何规范的换向关系。作为应用程序，我们重新考虑了规范的换向关系和场地的量化，以更加完整。
Inspired by the geometric bracket for the generalized covariant Hamilton system, we abstractly define a generalized geometric commutator $$\left[ a,b \right]={{\left[ a,b \right]}_{cr}}+G\left(s,a,b \right)$$ formally equipped with geomutator $G\left(s, a,b \right)=a{{\left[ s,b \right]}_{cr}}-b{{\left[ s,a \right]}_{cr}}$ defined in terms of structural function $s$ related to the structure of spacetime or manifolds itself for revising the classical representation ${{\left[ a,b \right]}_{cr}}=ab-ba$ for any elements $a$ and $b$ of any algebra. Then we use the generalized geometric commutator to define quantum covariant Poisson bracket that is related to the quantum geometric bracket defined by geomutator as a generalization of quantum Poisson bracket. The covariant dynamics includes the generalized Heisenberg equation as a natural extension of Heisenberg equation and G-dynamics based on the quantum geometric bracket, meanwhile, the geometric canonical commutation relation is induced. As an application, we reconsider the canonical commutation relation and the quantization of field to be more complete.
