A Course in Mathematical Physics 1

1. Front Matter

   Pages i-xii

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2. Introduction

   • Walter Thirring, Evans Harrell

   Pages 1-7

3. Analysis on Manifolds

   • Walter Thirring, Evans Harrell

   Pages 8-75

4. Hamiltonian Systems

   • Walter Thirring, Evans Harrell

   Pages 76-141

5. Nonrelativistic Motion

   • Walter Thirring, Evans Harrell

   Pages 142-184

6. Relativistic Motion

   • Walter Thirring, Evans Harrell

   Pages 185-234

7. The Structure of Space and Time

   • Walter Thirring, Evans Harrell

   Pages 235-250

8. Back Matter

   Pages 251-258

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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 intro­ 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 pre­ 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 rela­ tivistic quantum theory, have not yet matured from the stage of rules for calculations to mathematically well understood disciplines, and are there­ 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 mathe­ matics.

• mathematical physics

• Institute for Theoretical Physics, University of Vienna, Austria

  Walter Thirring

• Massachusetts Institute of Technology, Cambridge, USA

  Evans Harrell

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