Linked e-resources
Details
Table of Contents
Preface to the Second Edition; Preface to the First Edition; Contents; Notation and Conventions; 1 Sketch of Lagrangian Formalism; 1.1 Newton's Equation; 1.2 Galilean Transformations: Principle of Galilean Relativity; 1.3 Poincaré and Lorentz Transformations: The Principle of Special Relativity; 1.4 Principle of Least Action; 1.4.1 Variational Analysis; 1.4.2 Generalized Coordinates, Coordinate Transformations and Symmetries of an Action; 1.5 Examples of Continuous (Field) Systems; 1.6 Action of a Constrained System; 1.6.1 The Recipe; 1.6.2 Justification of the Recipe.
1.6.3 Description of Constrained System by Singular Action1.6.4 Kinetic Versus Potential Energy: Forceless Mechanics of Hertz; 1.7 Electromagnetic Field in Lagrangian Formalism; 1.7.1 Maxwell Equations; 1.7.2 Nonsingular Lagrangian Action of Electrodynamics; 1.7.3 Manifestly Poincaré-Invariant Formulation in Terms of a Singular Lagrangian Action; 1.7.4 Notion of Local (Gauge) Symmetry; 1.7.5 Lorentz Transformations of Three-Dimensional Potential: Role of Gauge Symmetry; 1.7.6 Relativistic Particle in Electromagnetic Field; 1.7.7 Speed of Light and Critical Speed in External Field.
1.7.8 Poincaré Transformations of Electricand Magnetic Fields2 Hamiltonian Formalism; 2.1 Derivation of Hamiltonian Equations; 2.1.1 Preliminaries; 2.1.2 From Lagrangian to Hamiltonian Equations; 2.1.3 Short Prescription for Hamiltonization Procedure, Physical Interpretation of Hamiltonian; 2.1.4 Inverse Problem: From Hamiltonian to Lagrangian Formulation; 2.2 Poisson Bracket and Symplectic Matrix; 2.3 General Solution to Hamiltonian Equations; 2.4 Picture of Motion in Phase Space; 2.5 Conserved Quantities and the Poisson Bracket; 2.6 Phase Space Transformations and Hamiltonian Equations.
2.7 Definition of Canonical Transformation2.8 Generalized Hamiltonian Equations: Example of Non-canonical Poisson Bracket; 2.9 Hamiltonian Action Functional; 2.9.1 Schrödinger Equation as the Hamiltonian System; 2.9.2 Lagrangian Action Associated with the Schrödinger Equation. Analogies Between Quantum Mechanics and Electrodynamics; 2.9.3 Probability as a Conserved Charge via the Noether Theorem; 2.9.4 First-Order Action Functional, Routhian and All That; 2.10 Hamiltonization of a Theory with Higher-Order Derivatives; 2.10.1 First-Order Trick; 2.10.2 Ostrogradsky Method.
3 Canonical Transformations of Two-Dimensional Phase Space3.1 Time-Independent Canonical Transformations; 3.1.1 Time-Independent Canonical Transformations and Symplectic Matrix; 3.1.2 Generating Function; 3.2 Time-Dependent Canonical Transformations; 3.2.1 Canonical Transformations and Symplectic Matrix; 3.2.2 Generating Function; 4 Properties of Canonical Transformations; 4.1 Invariance of the Poisson Bracket (Symplectic Matrix); 4.2 Infinitesimal Canonical Transformations: Hamiltonian as a Generator of Evolution; 4.2.1 Generator of Infinitesimal Canonical Transformation.
1.6.3 Description of Constrained System by Singular Action1.6.4 Kinetic Versus Potential Energy: Forceless Mechanics of Hertz; 1.7 Electromagnetic Field in Lagrangian Formalism; 1.7.1 Maxwell Equations; 1.7.2 Nonsingular Lagrangian Action of Electrodynamics; 1.7.3 Manifestly Poincaré-Invariant Formulation in Terms of a Singular Lagrangian Action; 1.7.4 Notion of Local (Gauge) Symmetry; 1.7.5 Lorentz Transformations of Three-Dimensional Potential: Role of Gauge Symmetry; 1.7.6 Relativistic Particle in Electromagnetic Field; 1.7.7 Speed of Light and Critical Speed in External Field.
1.7.8 Poincaré Transformations of Electricand Magnetic Fields2 Hamiltonian Formalism; 2.1 Derivation of Hamiltonian Equations; 2.1.1 Preliminaries; 2.1.2 From Lagrangian to Hamiltonian Equations; 2.1.3 Short Prescription for Hamiltonization Procedure, Physical Interpretation of Hamiltonian; 2.1.4 Inverse Problem: From Hamiltonian to Lagrangian Formulation; 2.2 Poisson Bracket and Symplectic Matrix; 2.3 General Solution to Hamiltonian Equations; 2.4 Picture of Motion in Phase Space; 2.5 Conserved Quantities and the Poisson Bracket; 2.6 Phase Space Transformations and Hamiltonian Equations.
2.7 Definition of Canonical Transformation2.8 Generalized Hamiltonian Equations: Example of Non-canonical Poisson Bracket; 2.9 Hamiltonian Action Functional; 2.9.1 Schrödinger Equation as the Hamiltonian System; 2.9.2 Lagrangian Action Associated with the Schrödinger Equation. Analogies Between Quantum Mechanics and Electrodynamics; 2.9.3 Probability as a Conserved Charge via the Noether Theorem; 2.9.4 First-Order Action Functional, Routhian and All That; 2.10 Hamiltonization of a Theory with Higher-Order Derivatives; 2.10.1 First-Order Trick; 2.10.2 Ostrogradsky Method.
3 Canonical Transformations of Two-Dimensional Phase Space3.1 Time-Independent Canonical Transformations; 3.1.1 Time-Independent Canonical Transformations and Symplectic Matrix; 3.1.2 Generating Function; 3.2 Time-Dependent Canonical Transformations; 3.2.1 Canonical Transformations and Symplectic Matrix; 3.2.2 Generating Function; 4 Properties of Canonical Transformations; 4.1 Invariance of the Poisson Bracket (Symplectic Matrix); 4.2 Infinitesimal Canonical Transformations: Hamiltonian as a Generator of Evolution; 4.2.1 Generator of Infinitesimal Canonical Transformation.