MICRO-MACRO DUALITY AND AN ATTEMPT TOWARDS MEASUREMENT SCHEME OF QUANTUM FIELDS

摘要

Here I consider the problem of consolidating the well-known heuristic idea of "quantum-classical correspondence", according to which macroscopic clas-sical objects are to be regarded as condensates of infinite quanta emerging from a microscopic quantum system. This attempt is for the purpose of es-tablishing effective mathematical methods or guiding principles for control-ling bi-directional transitions between microscopic quantum systems and macroscopic classical levels, whose essence can be boiled down into such an expression as "Micro-Macro duality", mathematically formulated as cate-gorical adjunctions found at many different levels in physical theories. This will be seen just a mathematically polished version of the above old heuris-tics, quantum-classical correspondence (q-c correspondence, for short), in physics. As exemplified by such interesting phenomena as "macroscopic quantum effects", the contrasts between [Micro vs. Macro] (according to length scales) and between [Quantum vs. Classical] (due to the essential dif-ferences of structures) are, precisely speaking, independent of each other to certain extent, owing to the absence of an intrinsic length scale to separate quantum and classical domains. Since this kind of mixtures can be taken as exceptional, however, I restrict my consideration here to such generic situations that processes taking place at microscopic levels are of quantum nature and that the macroscopic levels are described in the standard frame-work of classical physics, unless the considerations on the last point become crucial. On this premise of the parallelisms among micro/quantum/non-commutative and macro/classical/commutative, respectively, the essential contents of q-c correspondence involve the following two levels.