Author | Thirring, Walter. author |
---|---|

Title | A Course in Mathematical Physics 1 [electronic resource] : Classical Dynamical Systems / by Walter Thirring, Evans Harrell |

Imprint | Vienna : Springer Vienna, 1978 |

Connect to | http://dx.doi.org/10.1007/978-3-7091-8526-1 |

Descript | XII, 258 p. online resource |

SUMMARY

This textbook presents mathematical physics in its chronological order. It originated in a four-semester course I offered to both mathematicians and physicists, who were only required to have taken the conventional introยญ ductory courses. In order to be able to cover a suitable amount of advanced materil;ll for graduate students, it was necessary to make a careful selection of topics. I decided to cover only those subjects in which one can work from the basic laws to derive physically relevant results with full mathematical rigor. Models which are not based on realistic physical laws can at most serve as illustrations of mathematical theorems, and theories whose preยญ dictions are only related to the basic principles through some uncontrollable approximation have been omitted. The complete course comprises the following one-semester lecture series: I. Classical Dynamical Systems II. Classical Field Theory III. Quantum Mechanics of Atoms and Molecules IV. Quantum Mechanics of Large Systems Unfortunately, some important branches of physics, such as the relaยญ tivistic quantum theory, have not yet matured from the stage of rules for calculations to mathematically well understood disciplines, and are thereยญ fore not taken up. The above selection does not imply any value judgment, but only attempts to be logically and didactically consistent. General mathematical knowledge is assumed, at the level of a beginning graduate student or advanced undergraduate majoring in physics or matheยญ matics

CONTENT

1 Introduction -- 1.1 Equations of Motion -- 1.2 The Mathematical Language -- 1.3 The Physical Interpretation -- 2 Analysis on Manifolds -- 2.1 Manifolds -- 2.2 Tangent Spaces -- 2.3 Flows -- 2.4 Tensors -- 2.5 Differentiation -- 2.6 Integration -- 3 Hamiltonian Systems -- 3.1 Canonical Transformations -- 3.2 Hamiltonโ{128}{153}s Equations -- 3.3 Constants of Motion -- 3.4 The Limit t ? I ยฑ ? -- 3.5 Perturbation Theory: Preliminaries -- 3.6 Perturbation Theory: The Iteration -- 4 Nonrelativistic Motion -- 4.1 Free Particles -- 4.2 The Two-Body Problem -- 4.3 The Problem of Two Centers of Force -- 4.4 The Restricted Three-Body Problems -- 4.5 The N-body Problem -- 5 Relativistic Motion -- 5.1 The Hamiltonian Formulation of the Electrodynamic Equation of Motion -- 5.2 The Constant Field -- 5.3 The Coulomb Field -- 5.4 The Betatron -- 5.5 The Traveling Plane Disturbance -- 5.6 Relativistic Motion in a Gravitational Field -- 5.7 Motion in the Schwarzschild Field -- 5.8 Motion in a Gravitational Plane Wave -- 6 The Structure of Space and Time -- 6.1 The Homogeneous Universe -- 6.2 The Isotropic Universe -- 6.3 Me according to Galileo -- 6.4 Me as Minkowski Space -- 6.5 Me as a Pseudo-Riemannian Space

Mathematics
Mathematical physics
Physics
Mathematics
Mathematical Physics
Mathematical Methods in Physics
Theoretical Mathematical and Computational Physics