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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 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.
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, thermal quantum field theory (thermal field theory for short) or finite temperature field theory is a set of methods to calculate expectation values of physical observables of a quantum field theory at finite temperature.
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Schwinger parametrization is a technique for evaluating loop integrals which arise from Feynman diagrams with one or more loops. Using the well-known observation that 1 A n = 1 ( n − 1 ) ! ∫ 0 ∞ d u u n − 1 e − u A , {\displaystyle {\frac {1}{A^{n}}}={\frac {1}{(n-1)!}}\int _{0}^{\infty }du\,u^{n-1}e^{-uA},}