QVE method for solving electron-positron pairs creation in the vacuum

In the presence of an ultra-strong external field, the vacuum can generate electron-positron pairs, demonstrating that energy can be converted into mass. This generation process is of great significance for understanding the origin of matter. In recent years, with the rapid development of ultra-short and ultra-strong laser technology, the intensity of laser fields is gradually approaching the Schwinger threshold, which has prompted the application of different research methods and techniques in theoretical and numerical simulations of particle-pair production in vacuum. Among them, the quantum Vlasov equation (QVE) method is primarily used to solve the problem of electron-positron pair production in vacuum under a spatially uniform time-varying ultra-strong field. This paper reviews the proposal, development, and research progress of the QVE method, and introduces representative works. These studies not only provide valuable theoretical foundations for future verification experiments but also contribute to the research on antimatter and the understanding of the cosmic formation process under extreme conditions.