Schwinger model

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In physics, the Schwinger model, named after Julian Schwinger, is the model[1] describing 2D (1 spatial dimension + time) Euclidean quantum electrodynamics with a Dirac fermion. This model exhibits a spontaneous symmetry breaking of the U(1) symmetry due to a chiral condensate due to a pool of instantons. The photon in this model becomes a massive particle at low temperatures. This model can be solved exactly and is used as a toy model for other more complex theories.[2][3]

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 , instead of in 4 dimensions, 3 spatial, 1 time.


  1. ^ Schwinger, Julian (1962). Gauge Invariance and Mass. II. Physical Review, Volume 128. p. 2425. Bibcode:1962PhRv..128.2425S. doi:10.1103/PhysRev.128.2425. 
  2. ^ Schwinger, Julian (1951). The Theory of Quantized Fields I. Physical Review, Volume 82. p. 914. Bibcode:1951PhRv...82..914S. doi:10.1103/PhysRev.82.914. 
  3. ^ Schwinger, Julian (1953). The Theory of Quantized Fields II. Physical Review, Volume 91. p. 713. Bibcode:1953PhRv...91..713S. doi:10.1103/PhysRev.91.713.