LEADER 05059nam 22006495 450 001 9910254578103321 005 20200630132917.0 010 $a3-319-58298-4 024 7 $a10.1007/978-3-319-58298-6 035 $a(CKB)4340000000061862 035 $a(DE-He213)978-3-319-58298-6 035 $a(MiAaPQ)EBC6314697 035 $a(MiAaPQ)EBC5589169 035 $a(Au-PeEL)EBL5589169 035 $a(OCoLC)987794656 035 $a(PPN)201474964 035 $a(EXLCZ)994340000000061862 100 $a20170513d2017 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aClassical and Quantum Dynamics $eFrom Classical Paths to Path Integrals /$fby Walter Dittrich, Martin Reuter 205 $a5th ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017. 215 $a1 online resource (XVI, 489 p. 18 illus.) 311 $a3-319-58297-6 320 $aIncludes bibliographical references & index. 327 $aIntroduction -- 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 -- Appendix -- Solutions -- Index. 330 $aGraduate students who wish 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 fifth edition has been revised and enlarged to include chapters on quantum electrodynamics, in particular, Schwinger?s proper time method and the treatment of classical and quantum mechanics with Lie brackets and pseudocanonical transformations. It is shown that operator quantum electrodynamics can be equivalently described with c-numbers, as demonstrated by calculating the propagation function for an electron in a prescribed classical electromagnetic field. 606 $aQuantum theory 606 $aField theory (Physics) 606 $aMathematical physics 606 $aNuclear physics 606 $aQuantum Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19080 606 $aClassical and Continuum Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P2100X 606 $aMathematical Applications in the Physical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M13120 606 $aParticle and Nuclear Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P23002 615 0$aQuantum theory. 615 0$aField theory (Physics) 615 0$aMathematical physics. 615 0$aNuclear physics. 615 14$aQuantum Physics. 615 24$aClassical and Continuum Physics. 615 24$aMathematical Applications in the Physical Sciences. 615 24$aParticle and Nuclear Physics. 676 $a530.12 700 $aDittrich$b Walter$4aut$4http://id.loc.gov/vocabulary/relators/aut$046017 702 $aReuter$b Martin$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254578103321 996 $aClassical and Quantum Dynamics$9353281 997 $aUNINA