to Quantum Trajectories -- The Bohmian Route to the Hydrodynamic Equations -- The Phase Space Route to the Hydrodynamic Equations -- The Dynamics and Properties of Quantum Trajectories -- Function and Derivative Approximation on Unstructured Grids -- Applications of the Quantum Trajectory Method -- Adaptive Methods for Trajectory Dynamics -- Quantum Trajectories for Multidimensional Dynamics --…
Gaudin Model and Opers -- Integrable Models with Unstable Particles -- Quantum Reduction in the Twisted Case -- Representation Theory and Quantum Integrability -- Connecting Lattice and Relativistic Models via Conformal Field Theory -- Elliptic Spectral Parameter and Infinite-Dimensional Grassmann Variety -- Trigonometric Degeneration and Orbifold Wess-Zumino-Witten Model. II -- Weil-Petersson …
Kohn's Proof of the Hypoellipticity of the Hörmander Operators -- Compactness Criteria for the Resolvent of Schrödinger Operators -- Global Pseudo-differential Calculus -- Analysis of some Fokker-Planck Operator -- Return to Equillibrium for the Fokker-Planck Operator -- Hypoellipticity and Nilpotent Groups -- Maximal Hypoellipticity for Polynomial of Vector Fields and Spectral Byproducts -- …
Measures and Transforms -- Selfadjointness and Spectrum -- Criteria for Identifying the Spectrum -- Operators of Interest -- Applications.Themainobjectiveofthisbookistogiveacollectionofcriteriaavailablein the spectral theory of selfadjoint operators, and to identify the spectrum and its components in the Lebesgue decomposition. Many of these criteria were published in several articles in di?ere…
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…
The Unification Paradigm -- Standard Models of Physics and Cosmology -- Different Approaches: Quantum Superstrings and Quantum Gravity -- Other Approaches -- Fuzzy Spacetime and the Planck Scale -- The Universe of Fluctuations -- Quantum Geometry -- How Fundamental is Gravitation? -- The Elusive Mass Spectrum -- Experimental Effects.
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…