Classical and Quantum Dynamics [E-Book] : From Classical Paths to Path Integrals / by Walter Dittrich, Martin Reuter.
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...
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Full text |
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Personal Name(s): | Dittrich, Walter, author |
Reuter, Martin, author | |
Edition: |
6th edition 2020. |
Imprint: |
Cham :
Springer,
2020
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Physical Description: |
X, 563 pages 307 illustrations (online resource) |
Note: |
englisch |
ISBN: |
9783030367862 |
DOI: |
10.1007/978-3-030-36786-2 |
Subject (LOC): |
- 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.