05327nam 22006615 450 991038073620332120200705233614.03-030-36786-X10.1007/978-3-030-36786-2(CKB)4100000010480428(DE-He213)978-3-030-36786-2(MiAaPQ)EBC6112350(PPN)242981739(EXLCZ)99410000001048042820200206d2020 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierClassical and Quantum Dynamics From Classical Paths to Path Integrals /by Walter Dittrich, Martin Reuter6th ed. 2020.Cham :Springer International Publishing :Imprint: Springer,2020.1 online resource (X, 563 p. 307 illus.) 3-030-36785-1 Includes bibliographical references and index.Introduction -- The Action Principles in Mechanics -- The Action Principle in Classical Electrodynamics -- Application of the Action Principles -- Jacobi Fields, Conjugate Points.-Canonical Transformations -- The Hamilton–Jacobi Equation -- Action-Angle Variables -- The Adiabatic Invariance of the Action Variables -- Time-Independent Canonical Perturbation Theory -- Canonical Perturbation Theory with Several Degrees of Freedom -- Canonical Adiabatic Theory -- Removal of Resonances -- Superconvergent Perturbation Theory, KAM Theorem -- Poincaré Surface of Sections, Mappings -- The KAM Theorem -- Fundamental Principles of Quantum Mechanics -- Functional Derivative Approach -- Examples for Calculating Path Integrals -- Direct Evaluation of Path Integrals -- Linear Oscillator with Time-Dependent Frequency -- Propagators for Particles in an External Magnetic Field -- Simple Applications of Propagator Functions -- The WKB Approximation -- Computing the trace -- Partition Function for the Harmonic Oscillator -- Introduction to Homotopy Theory -- Classical Chern–Simons Mechanics -- Semiclassical Quantization -- The “Maslov Anomaly” for the Harmonic Oscillator.-Maslov Anomaly and the Morse Index Theorem -- Berry’s Phase -- Classical Geometric Phases: Foucault and Euler -- Berry Phase and Parametric Harmonic Oscillator -- Topological Phases in Planar Electrodynamics -- Path Integral Formulation of Quantum Electrodynamics -- Particle in Harmonic E-Field E(t) = Esinw0t; Schwinger-Fock Proper-Time Method -- The Usefulness of Lie Brackets: From Classical and Quantum Mechanics to Quantum Electrodynamics -- Green’s Function of a Spin-1/2 Particle in a Constant External Magnetic Field -- One-Loop Effective Lagrangian in QED -- On Riemann’s Ideas on Space and Schwinger’s Treatment of Low-Energy Pion-Nucleon Physics -- The Non-Abelian Vector Gauge Particle p -- Riemann’s Result and Consequences for Physics and Philosophy.Graduate students seeking to become familiar with advanced computational strategies in classical and quantum dynamics will find in this book both the fundamentals of a standard course and a detailed treatment of the time-dependent oscillator, Chern-Simons mechanics, the Maslov anomaly and the Berry phase, to name just a few topics. Well-chosen and detailed examples illustrate perturbation theory, canonical transformations and the action principle, and demonstrate the usage of path integrals. The sixth edition has been enlarged to include the Heisenberg-Euler Lagrangian, Schwinger’s source theory treatment of the low-energy π-ρ-N physics and general relativity, where Riemann’s (Einstein’s) ideas on space and time and their philosophical implications are discussed. .Quantum physicsContinuum physicsMathematical physicsNuclear physicsStatistical physicsQuantum Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P19080Classical and Continuum Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P2100XMathematical Applications in the Physical Scienceshttps://scigraph.springernature.com/ontologies/product-market-codes/M13120Particle and Nuclear Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P23002Statistical Physics and Dynamical Systemshttps://scigraph.springernature.com/ontologies/product-market-codes/P19090Quantum physics.Continuum physics.Mathematical physics.Nuclear physics.Statistical physics.Quantum Physics.Classical and Continuum Physics.Mathematical Applications in the Physical Sciences.Particle and Nuclear Physics.Statistical Physics and Dynamical Systems.530.12Dittrich Walterauthttp://id.loc.gov/vocabulary/relators/aut46017Reuter Martinauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910380736203321Classical and Quantum Dynamics353281UNINA