Photons in Fock Space and Beyond (in 3 Volumes)

ISBN-13: 9789814618823 / Angielski / Open Ebook / 2015 / 2352 str.

Reinhard Honegger; Alfred Rieckers

Opis

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.In Volume III, the mathematical tools for algebraic Quantum Electrodynamics (QED) are arranged in a form adapted to the needs of our physical elaborations in Volumes I and II. The treated disciplines of Mathematics could be studied independently, but the mentioned impacts on the physical applications may help to visualize and memorize the mathematical concepts, the terminology of which originating often from physical problems.The rather detailed exposition of C*- and von Neumann algebras should relieve the reader from consulting the pertinent text books in Mathematics and Mathematical Physics. Further topics comprise rigorous vector analysis with boundary conditions, measure theory on convex state spaces, dynamical perturbation theory over topological vector spaces and C*-algebras, and electrodynamic gauge theory.For studying this volume, a preliminary knowledge of Hilbert space mathematics, as used in courses on Quantum Mechanics, should be sufficient.