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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. [4]
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.
Schwinger's quantum action principle; Propagator; Annihilation operator; S-matrix; Standard Model; Local quantum physics; Nonlocal; Effective field theory; Correlation function (quantum field theory) Renormalizable; Cutoff; Infrared divergence, infrared fixed point; Ultraviolet divergence; Fermi's interaction; Path-ordering; Landau pole; Higgs ...
Download as PDF; Printable version; ... which commonly occur in the theory of differential equations, ... Schwinger's quantum action principle;
Path Integral Methods in Quantum Field Theories. Cambridge University Press. V.P. Nair (2005). Quantum Field Theory A Modern Perspective. Springer. There are some review article about applications of the Schwinger–Dyson equations with applications to special field of physics. For applications to Quantum Chromodynamics there are
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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]