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

机译:恢复弱等效原理的规范型旋转不变的非传感相空间

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We study the influence of noncommutativity of coordinates and noncommutativity of momenta on the motion of a particle (macroscopic body) in uniform and nonuniform 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 a gravitational field is determined by its mass. The trajectory of motion of a particle in a uniform gravitational field corresponds to the trajectory of a harmonic oscillator with frequency determined by the value of the parameter of momentum noncommutativity and mass of the particle. The equations of motion of a macroscopic body in a gravitational field depend on its mass and composition. From this follows a 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.
机译:我们研究了旋转对称的规范型非矫正相空间中颗粒(宏观重力场中颗粒(宏观重力场的运动的影响。结果表明,由于非组织性,粒子在引力场中的运动由其质量确定。均匀引力场中的颗粒运动的轨迹对应于谐振子的轨迹,其具有由频率非传闻和颗粒质量的参数的值确定的频率确定。宏观体在引力场中的运动方程依赖于其质量和组成。从这违反了非传统性引起的弱等效原则。我们得出结论,如果考虑到依赖质量的非传染性的张量,则在旋转不变的非传感空间中恢复弱等价原则。因此,最后我们构建了不规则的代数,它是旋转不变的,相当于规范类型的非态度代数,并不会导致违反弱等价原则。

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