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This model exhibits confinement of the fermions and as such, is a toy model for QCD. A handwaving argument why this is so is because in two dimensions, classically, the potential between two charged particles goes linearly as r {\displaystyle r} , instead of 1 / r {\displaystyle 1/r} in 4 dimensions, 3 spatial, 1 time.
In non-equilibrium physics, the Keldysh formalism or Keldysh–Schwinger formalism is a general framework for describing the quantum mechanical evolution of a system in a non-equilibrium state or systems subject to time varying external fields (electrical field, magnetic field etc.).
The Lippmann–Schwinger equation is useful in a very large number of situations involving two-body scattering. For three or more colliding bodies it does not work well because of mathematical limitations; Faddeev equations may be used instead. [4]
In addition to QCD in four spacetime dimensions, the two-dimensional Schwinger model also exhibits confinement. [9] Compact Abelian gauge theories also exhibit confinement in 2 and 3 spacetime dimensions. [10] Confinement has been found in elementary excitations of magnetic systems called spinons. [11]
In theoretical physics, the Rarita–Schwinger equation is the relativistic field equation of spin-3/2 fermions in a four-dimensional flat spacetime. It is similar to the Dirac equation for spin-1/2 fermions. This equation was first introduced by William Rarita and Julian Schwinger in 1941. In modern notation it can be written as: [1]
In Schwinger's approach, the action principle is targeted towards quantum mechanics. The action becomes a quantum action , i.e. an operator, S {\displaystyle S} . 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.
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The Schwinger–Dyson equations (SDEs) or Dyson–Schwinger equations, named after Julian Schwinger and Freeman Dyson, are general relations between correlation functions in quantum field theories (QFTs).