标题： 在牛顿时空中的测地线乘法与量子运动学 显示英文标题

标题： Geodesic multiplication and quantum kinematics in a Newtonian spacetime

摘要： 我们考虑在Cartan提出的非相对论时空框架下，处于牛顿引力场背景中的量子测试粒子。 我们提出了一种新颖的点粒子量化方法，即通过相应的黎曼规范坐标引入其位置算子，并通过时空点的测地乘法确定的无限小右平移算子引入动量算子。 我们对二维牛顿时空的最简单模型进行了详细的计算。 显示英文摘要

摘要： We consider a quantum test particle in the background of a Newtonian gravitational field in the framework of Cartan's formulation of nonrelativistic spacetimes. We have proposed a novel quantization of a point particle which amounts to introducing its position operators as multiplication with the corresponding Riemann normal coordinates and momentum operators as infinitesimal right translation operators determined by geodesic multiplication of points of the spacetime. We present detailed calculations for the simplest model of a two-dimensional Newtonian spacetime.