Operational Symmetries: Basic Operations in Physics

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. 

Table of Contents:
Introduction and Orientation.- Units and Orders of Magnitude.- How Complex is Nature?.- Plato’s Beautiful Symmetry.- Circles and Winding Numbers.- The Hall of Mirrors.- Telescopes for Symmetries.- Classical and Quantum Logics.- Classical and Quantum Probability.- Free States and Particles.- Operational Position and the Atomic Spectrum.- Operational Spacetime and the Particle Spectrum.

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.

Review :
“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)