The three-volume major reference "Photons in Fock Space and Beyond" undertakes a new mathematical and conceptual foundation of the theory of light emphasizing mesoscopic radiation systems. The quantum optical notions are generalized beyond Fock representations where the richness of an infinite dimensional quantum field system, with its mathematical difficulties and theoretical possibilities, is fully taken into account. It aims at a microscopic formulation of a mesoscopic model class which covers in principle all stages of the generation and propagation of light within a unified and well-defined conceptual frame.The dynamics of the interacting systems is founded - according to original works of the authors - on convergent perturbation series and describes the developments of the quantized microscopic as well as the classical collective degrees of freedom at the same time. The achieved theoretical unification fits especially to laser and microwave applications inheriting objective information over quantum noise.A special advancement is the incorporation of arbitrary multiply connected cavities where ideal conductor boundary conditions are imposed. From there arises a new category of classical and quantized field parts, apparently not treated in Quantum Electrodynamics before. In combination with gauge theory, the additional "cohomological fields" explain topological quantum effects in superconductivity. Further applications are to be expected for optoelectronic and optomechanical systems.
Volume I: From Classical to Quantized Radiation Systems: Solution Theory of Maxwell Equations in General Cavities; Cohomological Fields; Canonical Electrodynamics; C*-Algebraic Statistical Electrodynamics; Scattering Theory for Classical Fields; Canonical (Field) Quantization and Weyl Algebras; Quantized Maxwell Dynamics with Classical Sources; Photon Wave Functions and Fock Space; Finite Particles with Quantized Fields; Deformation Quantization and Operator Ordering; Infinite Heisenberg Group; Optical and Coherent States in and Beyond Fock Space; Volume II: Quantized Mesoscopic Radiation Models: Algebraic and Unitary Squeezing; Diagonalization of Field Hamiltonians; General Analysis of Squeezed States; Algebraic Black Body Radiation and Ergodic Theory; Mathematical Bloch Theory; Fermion Field Algebra; Particle-Hole Fields; Classical Extended Fermion Algebra; Mean Field Supporting States and Long Range Order; Weakly Inhomogeneous Cluster Interactions; Semiconductor-Photon Interactions; Weakly Inhomogeneous BCS Models and Josephson Junctions; Topological Effects for Junction Circuits; General Mesoscopic Radiation Models; Maxwell Dynamics as Collective Structure; Mesoscopic Dicke Models; Radiating Semiconductors; Josephson Oscillators; Microscopic and Macroscopic Quantum Structures; Volume III: Mathematics for Photon Fields Hilbert Space Operators; Sesquilinear Forms and Selfadjointness; Vector Analysis in Sobolev Spaces with Boundary Conditions; Non-Smooth Helmholtz-Hodge Decomposition Theory; *-Algebras; C*-Algebras; von Neumann Algebras; Modular Theory and Thermal Fields; Convex State Space Approach; Characterization of Quantum Theories; Orthogonal State Decompositions; Algebraic Ergodic Theory; Algebraic Transition Probabilities; Infinite Tensor Products; Locally Convex Spaces; Measures on Dual Spaces; Field Dynamics and Perturbation Theory; Manifolds and Fiber Bundles; Gauge Bundles for (Q)ED;