论文标题
洛伦兹不变的非交通时空的最大加速度
Maximal acceleration in a Lorentz invariant non-commutative space-time
论文作者
论文摘要
在本文中，我们将非交通性校正得出，以达到Doplicher-Fredenhagen-Roberts（DFR）时空的最大加速度，并表明非交换性的效果是降低交通量限制中最大加速度值的幅度。我们还使用阳性条件在通勤时空中最大加速度的幅度上沿着非交通坐标获得加速度上的上限。从地球方程的牛顿极限和线性化重力的爱因斯坦方程式中，我们在DFR时空中衍生出牛顿潜力的明确形式。通过表达最大加速度的非交通校正项，就牛顿的潜力和应用阳性条件而言，我们在DFR时空的重力吸引力下在两个颗粒之间的径向距离上获得了下限。由于存在最大加速度，我们还得出了修改的不确定性关系和坐标之间的换向关系。
In this paper, we derive the non-commutative corrections to the maximal acceleration in the Doplicher-Fredenhagen-Roberts (DFR) space-time and show that the effect of the non-commutativity is to decrease the magnitude of the value of the maximal acceleration in the commutative limit. We also obtain an upper bound on the acceleration along the non-commutative coordinates using the positivity condition on the magnitude of the maximal acceleration in the commutative space-time. From the Newtonian limit of the geodesic equation and Einstein's equation for linearised gravity, we derive the explicit form of Newton's potential in DFR space-time. By expressing the non-commutative correction term of the maximal acceleration in terms of Newton's potential and applying the positivity condition, we obtain a lower bound on the radial distance between two particles under the gravitational attraction in DFR space-time. We also derive modified uncertainty relation and commutation relation between coordinates and its conjugate, due to the existence of maximal acceleration.
