LEADER 05327nam 22006615 450 001 9910380736203321 005 20200705233614.0 010 $a3-030-36786-X 024 7 $a10.1007/978-3-030-36786-2 035 $a(CKB)4100000010480428 035 $a(DE-He213)978-3-030-36786-2 035 $a(MiAaPQ)EBC6112350 035 $a(PPN)242981739 035 $a(EXLCZ)994100000010480428 100 $a20200206d2020 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 $a6th ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020. 215 $a1 online resource (X, 563 p. 307 illus.) 311 $a3-030-36785-1 320 $aIncludes bibliographical references and 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 -- 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. 330 $aGraduate 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 ?-?-N physics and general relativity, where Riemann?s (Einstein?s) ideas on space and time and their philosophical implications are discussed. . 606 $aQuantum physics 606 $aContinuum physics 606 $aMathematical physics 606 $aNuclear physics 606 $aStatistical 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 606 $aStatistical Physics and Dynamical Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/P19090 615 0$aQuantum physics. 615 0$aContinuum physics. 615 0$aMathematical physics. 615 0$aNuclear physics. 615 0$aStatistical 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. 615 24$aStatistical Physics and Dynamical Systems. 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 $a9910380736203321 996 $aClassical and Quantum Dynamics$9353281 997 $aUNINA