Operational symmetries : basic operations in physics / Heinrich Saller.
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 nonrelativist...
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| Language: | English |
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| 100 | 1 | |a Saller, Heinrich, |e author. |0 http://id.loc.gov/authorities/names/n84211641 |1 http://isni.org/isni/000000011079501X. | |
| 245 | 1 | 0 | |a Operational symmetries : |b basic operations in physics / |c Heinrich Saller. |
| 264 | 1 | |a Cham : |b Springer, |c 2017. | |
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| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |a 1 Introduction and Orientation; 2 Units and Orders of Magnitude; 2.1 External Interactions and Newton's Unit; 2.2 Speed of Light as Space-Time Hinge; 2.3 Gravity and Maximal Speed of Action; 2.4 Quantum Structure and Planck's Unit; 2.5 Minimal Quantum of Action and Maximal Speed of Action; 2.6 Intrinsic Units; 2.7 The (hbar, c, G)-System -- Universal Units?; 2.8 Electrodynamics and Sommerfeld's Fine-Structure Constant; 2.9 Binding Energies and Couplings; 2.10 Electroweak Interactions; 2.11 Units and Symmetry Normalizations; 3 How Complex Is Nature?; 3.1 Numbers for Objects and Time. | |
| 505 | 8 | |a 3.2 Numbers as Operations -- From the Naturals to the Rationals3.3 Discrete and Continuous -- From the Rationals to the Reals; 3.4 Constancy in Change -- From the Real to the Complex Numbers; 3.5 Dynamics as Time Action; 3.6 Modalities; 3.7 Non-commutative Numbers -- Quaternions; 3.8 Non-commutative Complex Operations; 3.9 Causal Minkowski Spacetime; 3.10 Hypercharge Group and Isospin Group; 3.11 Lorentz Group and Poincaré Group; 3.12 Internal Scalar Product and External Lorentz Metric; 3.13 Operational Spacetime; 4 Plato's Beautiful Symmetry. | |
| 505 | 8 | |a 4.1 Regular Polygons and Platonic Triangles4.2 Platonic Solids; 4.3 Plato's Immaterial Basic Physics; 4.4 Dual Platonic Solids; 4.5 Soccer Molecules; 4.6 Coordinates for Platonic Solids; 4.7 Kepler's Mysterium Cosmographicum; 4.8 Polytopes and Mosaics; 4.9 Orthogonal Symmetry Groups; 4.10 Erlangen Program of Geometry; 4.11 Erlangen Program of Flat Space-Time; 4.12 Simple Lie Operations; 4.13 Lie Symmetries and Metrical Structures; 4.14 The Simplest Simple Symmetry; 4.15 Quantum Numbers and Weights of Simple Lie Algebras; 4.16 Weights, Roots, and Weyl Mirrors. | |
| 505 | 8 | |a 4.17 Decomposition of Product Representations4.18 Squares and the Physics of Atoms; 4.19 Plato's Polytopes and Cartan's Weight Diagrams; 4.20 Quark Flavors; 4.21 Plato's Triangles and Dynkin's Diagrams; 4.22 Fundamental Representations; 4.23 Quantum Theory and Symmetry; 4.24 Basic Internal Symmetry Program; 4.25 Basic External Symmetry Program; 5 Circles and Winding Numbers; 5.1 Circles on the Earth and in the Sky; 5.2 Winding Numbers and Unit Roots; 5.3 Electromagnetic Winding Numbers; 5.4 Energies and Time-Winding Numbers; 5.5 Spin Winding Numbers; 5.6 Windings of the Binary Alternative. | |
| 505 | 8 | |a 5.7 Charge Numbers of Leptons and Quarks5.8 Winding Number Matrices and Representation Weights; 5.9 Fractionality of Unitary Group Representations; 5.10 Adjoint Winding Numbers and Adjutopes; 5.11 Additive Unification of Unitary Symmetries; 5.12 Fractionality Correlations for Unitary Groups; 5.13 Broken Winding Numbers; 5.14 Broken Hypercharges and Nonabelian Internal Symmetry; 5.15 Young Frames for SU(n)-Representations; 5.16 Young Tableaux for Young Frames; 5.17 Box-Matrix Algebras; 5.18 Algebras for Finite Groups; 6 The Hall of Mirrors; 6.1 Reflection Group and Orthogonality. | |
| 520 | |a 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. | ||
| 588 | 0 | |a Online resource; title from PDF title page (EBSCO, viewed June 23, 2017) | |
| 650 | 0 | |a Symmetry (Physics) |0 http://id.loc.gov/authorities/subjects/sh85131443. | |
| 650 | 0 | |a Mathematical physics. |0 http://id.loc.gov/authorities/subjects/sh85082129. | |
| 650 | 0 | |a Quantum theory. |0 http://id.loc.gov/authorities/subjects/sh85109469. | |
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| 650 | 7 | |a Symmetry (Physics) |2 fast |0 (OCoLC)fst01140819. | |
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