Micro-Macro Duality in Quantum Physics

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. 1 Why & what is Micro-Macro Duality? – Vital roles played by Macro – In spite of their ubiquitous (but implicit) relevance to quantum theory, the importance of macroscopic classical levels is forgotten in current trends of microscopic quantum physics (owing to the overwhelming belief in the ultimate unification at the Planck scale?). Without those levels, however, neither measurement processes nor theoretical descriptions of microscopic quantum world would be possible! For instance, a state ω : A → C as one of the basic ingredients of quantum theory is nothing but a micromacro interface assigning macroscopically measurable expectation value Invited talk at International Conference on Stochastic Analysis, Classical and Quantum held in Nagoya in November 2004