The Development of the Action Principle

1. Front Matter

   Pages i-xv

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2. Curva Elastica

   • Walter Dittrich

   Pages 1-8

3. The Curva Elastica, a Curve of Least Energy

   • Walter Dittrich

   Pages 9-18

4. From Euler to Lagrange

   • Walter Dittrich

   Pages 19-20

5. Laplace and the Capillary—1807

   • Walter Dittrich

   Pages 21-26

6. A Final Application in Elasticity with Jacobi Elliptic Functions

   • Walter Dittrich

   Pages 27-32

7. Short List of Jacobi Elliptic Functions and Constants Used in Chap. 5

   • Walter Dittrich

   Pages 33-37

8. Variational Methods for Periodic Motions; Mathieu Functions

   • Walter Dittrich

   Pages 39-47

9. Lagrangian for Isentropic Irrotational Flow

   • Walter Dittrich

   Pages 49-56

10. Action Principle in Classical Electrodynamics

    • Walter Dittrich

    Pages 57-65

11. The Two Giants in Gravity: Einstein and Hilbert

    • Walter Dittrich

    Pages 67-78

12. The Quantum Action Principle

    • Walter Dittrich

    Pages 79-82

13. The Action Principle in Quantum Field Theory

    • Walter Dittrich

    Pages 83-91

14. Quantum Field Theory on Space-Like Hypersurfaces

    • Walter Dittrich

    Pages 93-97

15. Lagrangian Formulation of Gauge Theories

    • Walter Dittrich

    Pages 99-109

16. Effective Actions (Lagrangians) in Quantum Field Theory

    • Walter Dittrich

    Pages 111-116

17. Modified Photon Propagation Function, Source Theory

    • Walter Dittrich

    Pages 117-133

18. Back Matter

    Pages 135-135

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This book describes the historical development of the principle of stationary action from  the 17th to the 20th centuries. Reference is made to the most important contributors to this topic, in particular Bernoullis, Leibniz, Euler, Lagrange and Laplace. The leading theme is how the action principle is applied to problems in classical physics such as hydrodynamics, electrodynamics and gravity, extending also to the modern formulation of quantum mechanics and quantum field theory, especially quantum electrodynamics. A critical analysis of operator versus c-number field theory is given. The book contains many worked examples. In particular, the term "vacuum" is scrutinized.The book is aimed primarily at actively working researchers, graduate students and historians interested in the philosophical interpretation and evolution of physics; in particular, in understanding the action principle and its application to a wide range of natural phenomena.

• Action principle
• Curva elastica
• Elliptic functions
• Lagrangian in hydrodynamics
• Quantum action principle
• Gauge theories
• Quantum field theory
• Source theory vs. operator field theory
• History of Physics

• Institute of Theoretical Physics, University of Tübingen, Tübingen, Germany

  Walter Dittrich

Prof. Dr. Walter Dittrich was head of the quantum electrodynamics group at the University of Tübingen until his retirement in 2001 and is still actively publishing papers and books in classical and quantum physics. He received his doctorate under Prof. Heinz Mitter at Heisenberg’s institute in Munich and continued pre- and postdoc work at Brown University, Harvard and MIT. He profited immensely from lectures by and discussions with Profs. Herb Fried, Ken Johnson, Steve Weinberg, Julian Schwinger and, later on, at the Institute for Advanced Study (IAS) in Princeton, Steve Adler and David Gross at Princeton University. He started his work on gauge theories and QED in collaboration with Schwinger in the late 1960s. He was visiting professor at UCLA, Berkeley, Stanford and the IAS. He has over 30 years of teaching experience and is one of the key scientists in developing the theoretical framework of quantum electrodynamics. 

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