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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.).
Schwinger was a physics professor at several universities. Schwinger is recognized as an important physicist, responsible for much of modern quantum field theory, including a variational approach, and the equations of motion for quantum fields. He developed the first electroweak model, and the first example of confinement in 1+1 dimensions. He ...
Dyons were first proposed by Julian Schwinger in 1969 as a phenomenological alternative to quarks. [1] He extended the Dirac quantization condition to the dyon and used the model to predict the existence of a particle with the properties of the J/ψ meson prior to its discovery in 1974.
Over large times the vacuum expectation value of the Wilson loop projects out the state with the minimum energy, which is the potential between the quarks. [10] The excited states with energy V ( r ) + Δ E {\displaystyle V(r)+\Delta E} are exponentially suppressed with time and so the expectation value goes as
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.
Another class of methods is based on separable expansion of the potential or Green's operator like the method of continued fractions of Horáček and Sasakawa. Very important class of methods is based on variational principles, for example the Schwinger-Lanczos method combining the variational principle of Schwinger with Lanczos algorithm.
The Schwinger–Dyson equations (SDEs) or Dyson–Schwinger equations, named after Julian Schwinger and Freeman Dyson, ...