We propose the quantum field formalism as a new type of stochastic Markov process determined by local configuration. Our proposed Markov process is different with the classical one, in which the transition probability is determined by the state labels related to the character of state. In the new quantum Markov process, the transition probability is determined not only by the state character, but also by the occupation of the state. Due to the probability occupation of the state, the classical relation between the probability and condition probability at different times is no more valid. We have formulated the chain relation of successive transition for transition probability of the quantum Markov process instead of classical Chapman–Kolmogorov equation. The master equation is valid only in a classical Markov process. We have derived Euler-Lagrange equation in operator form as a characteristic equation of motion for the evolution of particle states as a Markov process.

我们提出量子场形式主义作为一种由局部配置决定的新型随机马尔可夫过程。我们提出的马尔可夫过程与经典的不同，其中转移概率由与状态特征相关的状态标签决定。在新的量子马尔可夫过程中，转移概率不仅由状态特征决定，还由状态的占有决定。由于状态的概率占用，不同时间的概率和条件概率之间的经典关系不再有效。我们为量子马尔可夫过程的跃迁概率制定了连续跃迁的链式关系，而不是经典的查普曼-柯尔莫哥洛夫方程。主方程仅在经典马尔可夫过程中有效。