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arXiv quant-ph/0108139quant-ph
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自由相对论粒子的随机力学

On the stochastic mechanics of the free relativistic particle

Michele Pavon

发表信息：
Journal of Mathematical Physics, 42 (2001), 4846-4856
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摘要：

给定Klein-Gordon方程的正能量解，自由、无自旋、相对论性粒子的运动在固定的洛伦兹坐标系中由具有非常数扩散系数的马尔可夫扩散过程描述。适当的时间是一个增加的随机过程，我们得到了一个概率推广的方程$(dτ)^2=-\frac{1}{c^2}dX_νdX_ν$。随机时变变换提供了$t$和$τ$域之间的桥梁。在$τ$域上，得到了一个具有奇异常扩散系数的$\M^4$值马氏过程. Klein-Gordon解的平方模是这个马尔可夫过程的不变的、不可积的密度。它满足相对论协变连续性方程。

英文摘要：

Given a positive energy solution of the Klein-Gordon equation, the motion of the free, spinless, relativistic particle is described in a fixed Lorentz frame by a Markov diffusion process with non-constant diffusion coefficient. Proper time is an increasing stochastic process and we derive a probabilistic generalization of the equation $(dτ)^2=-\frac{1}{c^2}dX_νdX_ν$. A random time-change transformation provides the bridge between the $t$ and the $τ$ domain. In the $τ$ domain, we obtain an $\M^4$-valued Markov process with singular and constant diffusion coefficient. The square modulus of the Klein-Gordon solution is an invariant, non integrable density for this Markov process. It satisfies a relativistically covariant continuity equation.

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