Operational symmetries : basic operations in physics /: basic operations in physics. (2017)

• Record Type: Book
• Further Information: Note: Heinrich Saller.
• Authors: Saller, Heinrich
• Contents: 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. 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. 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. 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. 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.
• Publisher Details: Cham : Springer
• Publication Date: 2017
• Extent: 1 online resource, illustrations
• Subjects: 539.7/25; Physics; Symmetry (Physics); Mathematical physics; Quantum theory; SCIENCE -- Physics -- Quantum Theory; Mathematical physics; Quantum theory; Symmetry (Physics); Science -- Quantum Theory; Mathematics -- Group Theory; Science -- Gravity; Science -- Mathematical Physics; Quantum physics (quantum mechanics & quantum field theory); Groups & group theory; Gravity; Mathematical physics; Topological Groups; Electronic books
• Languages: English
• ISBNs: 9783319586649; 3319586645
• Related ISBNs: 9783319586632; 3319586637
• Notes: Note: Includes bibliographical references and index.; Note: Online resource; title from PDF title page (EBSCO, viewed June 23, 2017).
• 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.