| Description |
1 online resource (153 pages) |
| Series |
UNIPA Springer Ser |
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UNIPA Springer series.
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| Contents |
Intro -- Foreword -- Preface -- Introduction -- General Context -- The Present Work -- Contents -- 1 Fundamental Assumptions -- 1.1 Basic Assumptions of Quantum Mechanics -- 1.2 Quantum States as Rays and Related Mathematical Concepts -- 2 The State of a Quantum System as a Subsystem of a Composite System -- 2.1 Non-probabilistic Characterization of the State of a Subsystem -- 2.2 Mathematical Characterization of Zurek's Envariance -- 2.3 Characterization of a State Through Its Properties -- 3 Relation Between the State of a System as Isolated and as Open |
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3.1 Representation of Isolated and Non-isolated Systems -- 3.2 Conditions for Density Operators -- 3.3 Physical Interpretation of Generic Density Operators -- 4 The Probability Law for Generic Density Operators -- 4.1 Mathematical Structure of a ̀̀Generic'' Density Operator -- 4.2 Universality of the Probability Distribution Function of a Generic Density Operator -- 4.3 A Functional Equation for g2 -- 4.4 Solution of the Functional Equation -- 4.5 The Function g for Arbitrary Rank -- Appendix A Categories -- A.1 The Categories of Sets -- A.2 The Category of G-Sets |
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A.2.1 Congruence. Invariant Sets -- A.2.2 Orbits. Stabilizer -- A.2.3 Generators. Frame -- Appendix B Barycentric Coordinates -- B.1 Simplexes and Systems of Linear Inequalities -- B.1.1 Consistent Sets in a Simplex -- Appendix C Linear Spaces -- C.1 Duals and Adjoints -- C.2 Free Vector Spaces -- C.2.1 Finite-Dimensional Free Vector Spaces -- C.3 Tensor Products -- C.3.1 Some Properties of Tensor Products Between Linear Spaces -- C.3.2 Linear Mappings Between Tensor Products -- Appendix D Mathematical Frameworks -- D.1 Hilbert Spaces -- D.1.1 Linear Mappings Between Hilbert Spaces |
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D.1.2 Tensor Products. Universal Property -- D.2 Canonical Factorization -- D.3 Hilbert-Schmidt Spaces -- D.3.1 Orbits. Spectra -- D.4 Class of Hilbert Spaces as a Category -- D.5 System and Environment -- D.6 Measurement -- D.7 Stabilizer -- Appendix References |
| Summary |
This book presents a selection of Prof. Matteo Campanellas writings on the interpretative aspects of quantum mechanics and on a possible derivation of Born's rule - one of the key principles of the probabilistic interpretation of quantum mechanics - that is independent of any priori probabilistic interpretation. This topic is of fundamental interest, and as such is currently an active area of research. Starting from a natural method of defining such a state, Campanella found that it can be characterized through a partial density operator, which occurs as a consequence of the formalism and of a number of reasonable assumptions connected with the notion of a state. The book demonstrates that the density operator arises as an orbit invariant that has to be interpreted as probabilistic, and that its quantitative implementation is equivalent to Born's rule. The appendices present various mathematical details, which would have interrupted the continuity of the discussion if they had been included in the main text. For instance, they discuss baricentric coordinates, mapping between Hilbert spaces, tensor products between linear spaces, orbits of vectors of a linear space under the action of its structure group, and the class of Hilbert space as a category |
| Notes |
Print version record |
| Subject |
Quantum theory.
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Mathematical physics.
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Quantum Theory
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Quantum physics (quantum mechanics & quantum field theory)
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Mathematical modelling.
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Science -- Quantum Theory.
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Mathematics -- Applied.
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Matemáticas -- Estadística aplicada
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Quanta, Teoría de los
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Mathematical physics
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Quantum theory
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| Form |
Electronic book
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| Author |
Jou, D. (David)
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Mongiovì, Maria Stella
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| ISBN |
9783030442071 |
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3030442071 |
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