量子物理中的微观-宏观对偶性

摘要：

微观-宏观对偶性在这里指的是微观量子世界和各种宏观经典能级之间的普遍相互关系，它可以在数学上表述为范畴的相互关系。它是基于我在2003年提出的选择准则的广义扇区统一方案的基础，从统一的角度控制物理学的不同分支，这在将Doplicer-Haag-Roberts超选择理论扩展到各种自发以及显式破缺对称性的情况中发挥了重要作用。沿着这条思路，测量所需的系统和测量仪器之间的状态关联可以在群对偶的背景下规范地制定;所获得的测量方案不限于有限数量粒子的量子力学情况，但可以安全地应用于具有无限自由度的量子场论，其局部子代数由III型冯诺依曼代数给出。

英文摘要：

Micro-Macro Duality means here the universal mutual relations between the microscopic quantum world and various macroscopic classical levels, which can be formulated mathematically as categorical adjunctions. It underlies a unified scheme for generalized sectors based upon selection criteria proposed by myself in 2003 to control different branches of physics from a unified viewpoint, which has played essential roles in extending the Doplicher-Haag-Roberts superselection theory to various situations with spontaneously as well as explicitly broken symmetries. Along this line of thought, the state correlations between a system and a measuring apparatus necessary for measurements can canonically be formulated within the context of group duality; the obtained measurement scheme is not restricted to the quantum mechanical situations with finite number of particles but can safely be applied to quantum field theory with infinite degrees of freedom whose local subalgebras are given by type III von Neumann algebras.

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