Quantum Measure Theory (Fundamental Theories of Physics)
Editorial Reviews
Book Description
This book is the first systematic treatment of measures on projection lattices of von Neumann algebras. It presents significant recent results in this field. One part is inspired by the Generalized Gleason Theorem on extending measures on the projection lattices of von Neumann algebras to linear functionals. Applications of this principle to various problems in quantum physics are considered (hidden variable problem, Wigner type theorems, decoherence functional, etc.). Another part of the monograph deals with a fascinating interplay of algebraic properties of the projection lattice with the continuity of measures (the analysis of Jauch-Piron states, independence conditions in quantum field theory, etc.). These results have no direct analogy in the standard measure and probability theory. On the theoretical physics side, they are instrumental in recovering technical assumptions of the axiomatics of quantum theories only by considering algebraic properties of finitely additive measures (states) on quantum propositions.
Book Info
Text discusses measures on projection lattices of von Neumann algebras, presenting significant recent results in the field. For readers interested in operator theory and functional analysis, measure and probability theory, and mathematical foundations of quantum theory and their interpretations. Includes index and references.
Quantum Measure Theory (Fundamental Theories of Physics),J. Hamhalter,Springer,1402017146,Calculus,Mathematical Analysis,Mathematics,Physics,Quantum measure theory,Science,Science/Mathematics,Mathematics / Mathematical Analysis
Books Info:
Recommended Books