On quantum solitons and their classical relatives: Reducible quantum fields and infinite constituent ‘‘elementary’’ systems

摘要: We demonstrate that the emergence of translation modes in quantization some at least nonlinear field theory models (like, e.g., φ4 or sine–Gordon systems) implies a specific structure their state spaces namely this direct integral Hilbert space, which follows from reducibility involved quantum canonical commutation relations (CCR) algebras. As special manifestation structure, one recovers infinite constituent ‘‘elementary’’ systems living commutant CCR algebra, appear as Schrodinger two level ones. The corresponding Hamiltonians are derived. In addition, we propose modification standard infrared (photon field) space construction employed electrodynamics. that, principle, Fermi (CAR) generators, carrying spin–charge–momentum labels Dirac particles, can be defined operators electromagnetic space. photon algebra is highly ...