Quantum Measures and Spaces

Quantum Measures and Spaces

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This book has evolved from lectures and seminars given by the author at different academic institutions during the years 1983-1998. It can be divided into four parts. Noncommutative measure theory is the theme of the first part of the book. The relevant quantum structures are algebraically introduced. This is then used in the axiomatic, geometric model discussed in the second part of the book, where old and partly new groups and finite-dimensional, -spaces or spheres are studied for particle-series, a bag and the four basic interactions of physics. The third part investigates infinite dimensional spaces, particularly Archimedean and non-Archimedean orthomodular spaces, which generalize classical Hilbert spaces. The last part of the book contains short reviews on related topics which are useful to have at hand. This volume should be of interest to graduate students and researchers whose work involves mathematics of physics relativity and gravitation, order, lattices, and algebraic structures.
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Product details

  • Hardback | 360 pages
  • 165.1 x 230 x 25.4mm | 703.07g
  • Dordrecht, Netherlands, United States
  • English
  • 0792352882
  • 9780792352884

Table of contents

Preface. I: Measures, Orthomodularity and Inner Products. 1. Introduction. 2. Orthomodular Measures. 3. Gleason's Theorem. 4. Gleason's Theorem in Applications; A. Dvurecenskij. 5. Inner Products. II: Matrix Operators and Particles. 6. Manifolds, Matrices and Lie Structures. 7. CC-Springs. 8. Spins. 9. Gravitons and 4D-Bags. III: Orthomodular Structures. 10. Complete Structures. 11. Dimension Theory. 12. Measures on Complete Structures. 13. Coordinatizations. 14. The Kakutani-Mackey Theorem. 15. Keller Spaces. 16. Orthomodular Spaces. IV: Miscellaneous. 17. About the 3-Sphere. 18. Spectral Theore; A. Hermann. 19. Topology. 20. Strong and Weak Topologies; P. Hitzler. 21. D-Posets and Effect Algebras; Z. Riecanová. V: Appendix. A. Anti-Automorphisms. B. Boolean Logic. C. Groups and General Algebras. D. 6-Roll Mill. E. Sets. F. Relativistic Quantum Mechanics. Bibliography. Index.
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About G. Kalmbach

`G. Kalmbach became a member of the elite society `Order of International Ambassadors'; carries the noble title `H.E.'; received from ABI USA, a Medal of Honour `2000 Millennium'; and from IBC England, the Gold Gilt Medal Award for `Outstanding People of the 20th Century', one of only 500 such medals awarded around the world.'
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