Abstract
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.
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This research was supported by the National Key Research and Development Program of China under Grants No. 2016YFB0700102, the National Natural Science Foundation of China under Grants No. 11774195.
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Ni, J. Quantum Field Theory Formulated as a Markov Process Determined by Local Configuration. Found Phys 51, 74 (2021). https://doi.org/10.1007/s10701-021-00481-6
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DOI: https://doi.org/10.1007/s10701-021-00481-6