论文标题
P-Adic量子力学中的微量类类操作员和状态
Trace class operators and states in p-adic quantum mechanics
论文作者
论文摘要
在量子力学的框架内，在p-adic数字的非架构数字的二次扩展上，我们提供了依赖一般代数方法的量子状态的定义以及概率理论的P-ADIC模型。与标准复杂情况一样，一组杰出的物理状态与某些有界运算符的痕迹概念有关，实际上，我们表明一个人也可以在非Archimedean设置中定义痕量类操作员的合适空间。分析了类似物，但也分析了复杂的希尔伯特空间中标准量子力学的情况。
Within the framework of quantum mechanics over a quadratic extension of the non-Archimedean field of p-adic numbers, we provide a definition of a quantum state relying on a general algebraic approach and on a p-adic model of probability theory. As in the standard complex case, a distinguished set of physical states are related to a notion of trace for a certain class of bounded operators and, in fact, we show that one can define a suitable space of trace class operators in the non-Archimedean setting, as well. The analogies, but also the several (highly non-trivial) differences, with respect to the case of standard quantum mechanics in a complex Hilbert space are analyzed.
