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Operational Symmetries

Basic Operations in Physics

  • Book
  • © 2017

Overview

Authors:
  1. Heinrich Saller

    1. Werner-Heisenberg Institute, Max Planck Institute for Physics, Munich, Germany

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  • Relates the particle spectrum with representations of operational electroweak spacetime
  • Explains infinite-dimensional spaces and continuous “quantum numbers”, necessary and characteristic for unitary faithful representations of noncompact groups
  • Highly experienced author, working over 40 years in mathematical physics with a special focus on field theory
  • Includes supplementary material: sn.pub/extras

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xi
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  2. Introduction and Orientation

    • Heinrich Saller
    Pages 1-11

  3. Units and Orders of Magnitude

    • Heinrich Saller
    Pages 13-49

  4. How Complex Is Nature?

    • Heinrich Saller
    Pages 51-92

  5. Plato’s Beautiful Symmetry

    • Heinrich Saller
    Pages 93-158

  6. Circles and Winding Numbers

    • Heinrich Saller
    Pages 159-200

  7. The Hall of Mirrors

    • Heinrich Saller
    Pages 201-232

  8. Telescopes for Symmetries

    • Heinrich Saller
    Pages 233-319

  9. Classical and Quantum Logics

    • Heinrich Saller
    Pages 321-353

  10. Classical and Quantum Probability

    • Heinrich Saller
    Pages 355-423

  11. Free States and Particles

    • Heinrich Saller
    Pages 425-468

  12. Operational Position and the Atomic Spectrum

    • Heinrich Saller
    Pages 469-505

  13. Operational Spacetime and the Particle Spectrum

    • Heinrich Saller
    Pages 507-566

  14. Back Matter

    Pages 567-574
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Keywords

About this book

This book describes the endeavour to relate the particle spectrum with representations of operational electroweak spacetime, in analogy to the atomic spectrum as characterizing representations of hyperbolic space. The spectrum of hyperbolic position space explains the properties of the nonrelativistic atoms; the spectrum of electroweak spacetime is hoped to explain those of the basic interactions and elementary particles.  



In this book, the theory of operational symmetries is developed from the numbers, from Plato’s and Kepler’s symmetries over the simple Lie groups to their applications in nonrelativistic, special relativistic and general relativistic quantum theories with the atomic spectrum for hyperbolic position and, in first attempts, the particle spectrum for electroweak spacetime.  

The standard model of elementary particles and interactions is characterized by a symmetry group. In general, as initiated by Weyl and stressed by Heisenberg, quantum theory can be built as a theory of operation groups and their unitary representations. In such a framework, time, position and spacetime is modeled by equivalence classes of symmetry groups. For a unification on this road, the quest is not for a final theory with a basic equation for basic particles, but for the basic operation group and its representations. 


Reviews

“This book is devoted to the symmetry that is one of the basic questions in Physics. … The author uses a comprehensible language to explain very complex phenomena connected with the symmetry. … There exist a lot of examples illustrating the theories. All above mentioned topics are written readably, and at the same time follow the academic frames with some simple proofs and corollaries.” (Dimitar A. Kolev, zbMATH 1381.81007, 2018)

Authors and Affiliations

  • Werner-Heisenberg Institute, Max Planck Institute for Physics, Munich, Germany

    Heinrich Saller

About the author

Prof. Dr. Heinrich Saller worked for over 40 years in mathematical physics with a special focus on field theory. His research interests include centrum correlations of the nonabelian internal symmetries isospin and colour with the abelian hypercharge; particle projection of relativistic fields and last but not least timespace as homogenous causal manifolds and their representations. He has worked at Cornell University and at the Ludwigs Maximilan University Munich (LMU). Heinrich Saller's main affiliation is the Max Planck Institute of Physics in Munich. He is editor-in-chief of the International Journal of Theoretical Physics.

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