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Photons in Fock Space and Beyond cover

The three-volume series "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.

Volume I begins with classical Electrodynamics (ED) which is shaped into a form enabling later on its integration into the extended frame of nonrelativistic Quantum Electrodynamics (QED) based on algebraic quantum field theory. A solution theory of Maxwell equations in multiply connected spatial domains (cavities) is elaborated with ideal conductor boundary conditions. From there arises a new category of classical and quantized field parts, apparently not treated in QED before.

The transition to QED follows ideas of deformation quantization. The free photon wave functions and Hamiltonians refer to diagonalized ED. As a first radiation system, finitely many point charges in interaction with the (quantized) electrodynamic field is worked out. On the other hand, the states of the electrodynamic Weyl algebra are thoroughly investigated. Especially a general structure theory for also non-Fock and non-classical coherent states is executed.

This three-volume series is recommended for graduate students and researchers working in rigorous Electrodynamics, Quantum Optics and Quantum Field Theory in general.

Contents:
  • Preliminaries on Electromagnetism
  • Classical Electrodynamics in L2-Hilbert Spaces
  • Classical Electrodynamics in the Smeared Field Formalism
  • Statistical Classical Electrodynamics
  • Canonical Quantization and Weyl Algebras
  • Deformation Quantization
  • Optical States, Optical Coherence
Readership: This three-volume series is recommended for graduate students and researchers working in rigorous Electrodynamics, Quantum Optics and Quantum Field Theory in general.