论文标题
量子古典动力括号
Quantum-Classical Dynamical Brackets
论文作者
论文摘要
我们研究了从完整量子支架的部分经典限制中构建一般杂种量子古典支架的问题。引入混合组成产品，我们表明这样的支架是该产品的换向器。从中，我们可以看到混合括号将遵守雅各比的身份，而莱布尼兹规则只要合成产品是关联的。这表明属于与组成产物的关联亚词架的一组混合变量将具有一致的量子古典动力学。这限制了允许的量子古典相互作用的汉密尔顿人的类别。此外，我们表明纯量子或经典变量可以在一致的框架中相互作用，而文献中不受无关定理或混合变量的限制。在拟议的方案中，量子反应在经典运动方程中以量子依赖性术语表示。
We study the problem of constructing a general hybrid quantum-classical bracket from a partial classical limit of a full quantum bracket. Introducing a hybrid composition product, we show that such a bracket is the commutator of that product. From this we see that the hybrid bracket will obey the Jacobi identity and the Leibniz rule provided the composition product is associative. This suggests that the set of hybrid variables belonging to an associative subalgebra with the composition product will have consistent quantum-classical dynamics. This restricts the class of allowed quantum-classical interaction Hamiltonians. Furthermore, we show that pure quantum or classical variables can interact in a consistent framework, unaffected by no-go theorems in the literature or the restrictions for hybrid variables. In the proposed scheme, quantum backreaction appears as quantum-dependent terms in the classical equations of motion.
