论文标题
布朗运动以光的速度：洛伦兹不变的过程家族
Brownian motion at the speed of light: a Lorentz invariant family of processes
论文作者
论文摘要
我们最近引入了一个新的过程，其中描述了粒子，只能在普通3D物理空间中以光C的速度移动。随机改变方向的速度可以表示为半径C球体表面的点及其轨迹只能连接该品种的点。可以通过考虑从一个点到另一个点的跳跃（不连续变化）和表面上的连续速度轨迹来构建过程。我们遵循了第二个新策略，假设速度是通过球体表面上的维纳过程（仅在“休息框架”中的各向同性）描述的。使用ITO微积分和Lorentz提升规则，我们在这里成功地表征了整个Lorentz-Invariant过程。此外，我们强调并描述了3D物理空间中粒子的长期扩散行为的短期弹道行为。
We recently introduced a new family of processes which describe particles which only can move at the speed of light c in the ordinary 3D physical space. The velocity, which randomly changes direction, can be represented as a point on the surface of a sphere of radius c and its trajectories only may connect the points of this variety. A process can be constructed both by considering jumps from one point to another (velocity changes discontinuously) and by continuous velocity trajectories on the surface. We followed this second new strategy assuming that the velocity is described by a Wiener process (which is isotropic only in the 'rest frame') on the surface of the sphere. Using both Ito calculus and Lorentz boost rules, we succeed here in characterizing the entire Lorentz-invariant family of processes. Moreover, we highlight and describe the short-term ballistic behavior versus the long-term diffusive behavior of the particles in the 3D physical space.
