Walter Dittrich - The Development of the Action Principle: A Didactic History from Euler-Lagrange to Schwinger

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This work is devoted to the development of the history of the principle of stationary action. It will be divided into two parts: in the first, we will pay tribute to the founders of the action principle, while the second part provides many different worked-out, selected examples which cover in great detail the achievements between the seventeenth and the beginning of the twentieth century. It is exciting to see how the greatest scientists of their time struggled with a final, mathematically satisfying formulation. Foremost Daniel Bernoulli, Euler, dAlembert and Laplace shaped the history of the early development of the action principle. Later on, Lagrange, Hamilton and last, not least, Schwinger finalized and polished the early attempts to transform almost all of nature's formidable problems into one dynamical principle.

How this principle is put to work and how much we have learned since Eulers fundamental contributions to the lemniscate problem (which spurred Gau motivation to develop the elliptic functions) and his introduction of the first classical field theory, namely, of the mathematically founded theory of hydrodynamics, is the leading theme in the present work.

In the nineteenth and twentieth centuries, we see the action principle celebrating triumphs in all branches of classical and quantum theory. The discovery of Einsteins field equations in gravity by Hilbert via the action principle and all the other applications of the action principle in classical and quantum theories of modern times can be traced back to the magnificent achievements by Euler and his contemporaries, and are valid still today.

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