Setting the Stage -- Linear Algebra over the Complex Numbers -- Complex Scalar Product Spaces (a.k.a. Hilbert Spaces) -- Lie Groups and Lie Group Representations -- New Representations from Old -- Irreducible Representations and Invariant Integration -- Representations and the Hydrogen Atom -- The Algebra so(4) Symmetry of the Hydrogen Atom -- The Group SO(4) Symmetry of the Hydrogen Atom -- Pr…
Units and Vectors -- Kinematics -- Newton’s Laws -- Work and Energy -- Impulse, Momentum and Collisions -- System of Particles -- Rotation of Rigid Bodies -- Rolling and Static Equilibrium -- Central Force Motion -- Oscillatory Motion.Open AccessThis open access textbook takes the reader step-by-step through the concepts of mechanics in a clear and detailed manner. Mechanics is considered to …
Fresnel’s (Dragging) Coefficient as a Challenge to 19th Century Optics of Moving Bodies -- Poincaré’s Relativistic Theory of Gravitation -- Standing on the Shoulders of a Dwarf: General Relativity—A Triumph of Einstein and Grossmann’s Erroneous Entwurf Theory -- Before the Riemann Tensor: The Emergence of Einstein’s Double Strategy -- A Conjecture on Einstein, the Independent Reality…
Introduction and Overview (E. Bick, F.D. Steffen) -- Topological Concepts in Gauge Theories (F. Lenz) -- Aspects of BRST Quantization (J.W. van Holten) -- Chiral Anomalies and Toplogy (J. Zinn-Justin) -- Supersymmetric Solitons and Topology (M. Shifman) -- Forces From Connes`Geometry (T. Schücker).Application of the concepts and methods of topology and geometry have led to a deeper understandi…
The intriguing mechanism of spontaneous symmetry breaking is a powerful innovative idea at the basis of most of the recent developments in theoretical physics, from statistical mechanics to many-body theory to elementary particles theory; for infinitely extended systems a symmetric Hamiltonian can account for non symmetric behaviours, giving rise to non symmetric realizations of a physical syst…
The Stability of Matter: From Atoms to Stars -- Lower bound to the energy of complex atoms -- Improved Lower Bound on the Indirect Coulomb Energy -- Letter to the Editor -- Proof of the Stability of Highly Negative Ions in the Absence of the Pauli Principle -- Atomic and Molecular Negative Ions -- Bound on the maximum negative ionization of atoms and molecules -- Approximate Neutrality of Large…
Photon Scattering -- Lepton Scattering -- Quasi-Elastic Lepton-Quark Scattering -- The Hydrogen Atom -- Many Electron Atoms -- Hadrons -- Covalent and Ionic Bonding -- Intermolecular Forces -- Cold Neutron Scattering -- The Nuclear Force and the Deuteron -- Quantum Gases -- Quantum Liquids -- Metals -- Nuclei — Droplets of a Fermi Liquid -- Stars, Planets, and Asteroids -- Elementary Particle…
Maxwell and Schrödinger -- Lorentz, Pauli and Dirac -- Quantum Fields and Particles -- Scattering and Bound States -- Hyperfine Shifts, Radiation, Quarks.In this book, quantum mechanics is developed from the outset on a relativistic basis, using the superposition principle, Lorentz invariance and gauge invariance. Nonrelativistic quantum mechanics as well as classical relativistic mechanics ap…
Elements of Quantum Dynamics -- Electron-Impurity System -- Linear Response Theory -- Bosons Interacting with Electrons -- Interacting Phonon Systems -- Effects of Electron-Electron Interaction -- Non-Equilibrium Electrons -- Non-Equilibrium Diagram Technique -- Kinetics of Bounded Systems -- Quantum Magnetotransport -- Photoexcitation -- Ballistic and Hopping Transport -- Multi-Channel Kinetic…
Noncommutative Geometry -- Poisson Geometry and Deformation Quantization -- Applications in Physics -- Topological Quantum Field Theory.This volume reflects the growing collaboration between mathematicians and theoretical physicists to treat the foundations of quantum field theory using the mathematical tools of q-deformed algebras and noncommutative differential geometry. A particular challeng…