Fock尺度下Q适应的量子随机积分和微分
Q-Adapted Quantum Stochastic Integrals and Differentials in Fock Scale
摘要：
本文首先介绍了量子随机积分的Fock-Guichardet形式，然后在正则基上引入了动力学的四个基本过程作为时空上QS积分的算子值测度。然后对QS积分进行了严格的分析，证明了QS导数的连续性。最后讨论了Q适应的量子动力学，包括玻色子Q=1，费米Q=-1，单调Q=0的量子动力学。这些可能是特别感兴趣的量子场论，量子开放系统，和量子理论的随机过程。
英文摘要：
In this paper we first introduce the Fock-Guichardet formalism for the quantum stochastic integration, then the four fundamental processes of the dynamics are introduced in the canonical basis as the operator-valued measures of the QS integration over a space-time. Then rigorous analysis of the QS integrals is carried out, and continuity of the QS derivative is proved. Finally, Q-adapted dynamics is discussed, including Bosonic Q=1, Fermionic Q=-1, and monotone Q=0 quantum dynamics. These may be of particular interest to quantum field theory, quantum open systems, and quantum theory of stochastic processes.
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