Interpretative aspects of quantum mechanics : Matteo Campanella's Mathematical Studies /: Matteo Campanella's Mathematical Studies. (2020)

• Record Type: Book
• Further Information: Note: Matteo Campanella, David Jou, Maria Stella Mongiovì.
• Other Names: Campanella, Matteo; Jou, D (David); Mongiovì, Maria Stella
• 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 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 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 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
• Publisher Details: Cham : Springer
• Publication Date: 2020
• Extent: 1 online resource (153 pages)
• Subjects: 530.12; 519; Quantum theory; Mathematical physics; Electronic books
• Languages: English
• ISBNs: 9783030442071; 3030442071
• Related ISBNs: 9783030442064
• Notes: Note: Description based on print version record.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.