Titlebook: Schwinger‘s Quantum Action Principle; From Dirac’s Formula Kimball A. Milton Book 2015 The Author(s) 2015 Julian Schwinger.Principle of Lea

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Time-Cycle or Schwinger-Keldysh Formulation,1964), and, rather mysteriously, cites the Martin-Schwinger equilibrium paper (Martin 1959), but not the nonequilibrium one (Schwinger 1961). The following was extracted from notes from Schwinger’s lectures given in 1968 at Harvard, as taken by the author.

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Historical Introduction,Euler (1744) the “principle of least action” was given modern form by de Maupertuis (1744, 1746). We will not attempt to trace the history here; a brief useful account is given in Sommerfeld’s lectures (Sommerfeld 1964). The most important names in the history of the development of dynamical systems

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Time-Cycle or Schwinger-Keldysh Formulation, nonequilibrium systems. Schwinger’s original work on this was his famous paper (Schwinger 1961); Keldysh’s paper appeared three years later (Keldysh 1964), and, rather mysteriously, cites the Martin-Schwinger equilibrium paper (Martin 1959), but not the nonequilibrium one (Schwinger 1961). The foll

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2191-5423 ’s Quantum Action Principle descended from Dirac’s formulation, which independently led Feynman to his path-integral formulation of quantum mechanics. Part I brings out in more detail the connection between the two formulations, and applications are discussed. Then, the Keldysh-Schwinger time-cycle

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