论四维弯曲时空中的正则方程及量子力学原理

On Canonical Equation and Principle of Quantum Mechanics in Four-dimensional Curved Space-time

根据哈密顿原理,利用等时变分法推导出四维弯曲时空中的测地线方程﹑拉格朗日方程﹑哈密顿正则方程以及拉格朗日函数与哈密顿函数。这些推论与广义相对论相对应的结论一致;过渡到非相对论时,其结论与经典力学一致。同时,根据哈密顿正则方程及相对论性矩阵力学,推导出四维弯曲时空中的矩阵力学方程。

According to the principle of Hamilton and isochronous variation,geodesic equation,Lagrange equation,Hamilton canonical equation,Lagrange function and Hamilton function in four-dimensional curved space-time are derived.These results are consistent with the corresponding conclusions of general relativity.When transited to classical mechanics,its conclusions are consistent with Newton’s theory of gravity.At the same time,according to Hamilton canonical equation and relativistic matrix mechanics,the quantum matrix mechanics equation in four-dimensional curved spacetime is given.