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In Schwinger's approach, the action principle is targeted towards quantum mechanics. The action becomes a quantum action, i.e. an operator, .Although it is superficially different from the path integral formulation where the action is a classical function, the modern formulation of the two formalisms are identical.
Schwinger's foundational work on quantum field theory constructed the modern framework of field correlation functions and their equations of motion. His approach started with a quantum action and allowed bosons and fermions to be treated equally for the first time, using a differential form of Grassman integration.
Action principles are the basis for Feynman's version of quantum mechanics, general relativity and quantum field theory. The action principles have applications as broad as physics, including many problems in classical mechanics but especially in modern problems of quantum mechanics and general relativity.
The action corresponding to the various paths is used to calculate the path integral, which gives the probability amplitudes of the various outcomes. Although equivalent in classical mechanics with Newton's laws, the action principle is better suited for generalizations and plays an important role in modern physics. Indeed, this principle is ...
This is the starting point of Schwinger’s treatment of the theory of quantum angular momentum, predicated on the action of these operators on Fock states built of arbitrary higher powers of such operators. For instance, acting on an (unnormalized) Fock eigenstate,
In physics, the Schwinger model, named after Julian Schwinger, is the model [1] describing 1+1D (1 spatial dimension + time) Lorentzian quantum electrodynamics which includes electrons, coupled to photons.
Therefore, the source appears in the vacuum amplitude acting from both sides on the Green's function correlator of the theory. [1] Schwinger's source theory stems from Schwinger's quantum action principle and can be related to the path integral formulation as the variation with respect to the source per se corresponds to the field , i.e. [6]
It is also referred to as the Sauter–Schwinger effect, Schwinger mechanism, or Schwinger pair production. It is a prediction of quantum electrodynamics (QED) in which electron – positron pairs are spontaneously created in the presence of an electric field, thereby causing the decay of the electric field.