标题： 具有弱等效原理恢复的规范型旋转不变非交换相空间 显示英文标题

标题： Rotationally invariant noncommutative phase space of canonical type with recovered weak equivalence principle

摘要： 我们研究了坐标与动量非对易性对粒子（宏观物体）在均匀和非均匀引力场中运动的影响，所考虑的相空间为保留旋转对称性的典型非对易相空间。 结果显示，由于非对易性，粒子在引力场中的运动由其质量决定。 均匀引力场中粒子的运动轨迹对应于具有由动量非对易参数值和粒子质量确定的频率的谐振子轨迹。 宏观物体在引力场中的运动方程依赖于其质量和组成。 由此得出结论，非对易性导致弱等效原理的违背。 我们得出结论，在旋转不变的非对易相空间中，若认为非对易张量依赖于质量，则弱等效原理得以恢复。 因此，最终我们构造了一个旋转不变的非对易代数，该代数等价于典型的非对易代数，并且不会导致弱等效原理的违背。 显示英文摘要

摘要： We study influence of noncommutativity of coordinates and noncommutativity of momenta on the motion of a particle (macroscopic body) in uniform and non-uniform gravitational fields in noncommutative phase space of canonical type with preserved rotational symmetry. It is shown that because of noncommutativity the motion of a particle in gravitational filed is determined by its mass. The trajectory of motion of a particle in uniform gravitational field corresponds to the trajectory of harmonic oscillator with frequency determined by the value of parameter of momentum noncommutativity and mass of the particle. The equations of motion of a macroscopic body in gravitational filed depend on its mass and composition. From this follows violation of the weak equivalence principle caused by noncommutativity. We conclude that the weak equivalence principle is recovered in rotationally invariant noncommutative phase space if we consider the tensors of noncommutativity to be dependent on mass. So, finally we construct noncommutative algebra which is rotationally invariant, equivalent to noncommutative algebra of canonical type, and does not lead to violation of the weak equivalence principle.