Quantum Measure Theory
By: by Jan Hamhalter
Series: Fundamental Theories of Physics, An International Book Series on The Fundamental Theories of Physics : Their Clarification, Development and Application -- 134; Fundamental Theories of Physics, An International Book Series on The Fundamental Theories of Physics : Their Clarification, Development and Application -- 134
Publisher: Springer Netherlands
Published: 2003
Place of publication: Dordrecht
Language: eng
Format: [electronic resource] /
Number of pages: 412
ISBN-13: 9789048164653; 9789401701198
Subjects: Functional analysis; Mathematics; Operator theory; Quantum theory
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.
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