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In physics, the '''Schwinger model''', named after [[Julian Schwinger]],  is the model<ref>{{Cite book  | last = Schwinger  | first = Julian  | authorlink =   | coauthors =   | title = Gauge Invariance and Mass. II | publisher = Physical Review, Volume 128  | date = 1962  | location =   | pages = 2425  | url =   | doi = 10.1103/PhysRev.128.2425  | id =   | isbn = }}</ref> describing 2D ''[[Euclidean space|Euclidean]]'' [[quantum electrodynamics]] with a [[Dirac spinor|Dirac fermion]]. This model exhibits a [[spontaneous symmetry breaking]] of the U(1) symmetry due to a [[chiral condensate]] due to a pool of [[instanton]]s. 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.<ref>{{Cite book  | last = Schwinger  | first = Julian  | authorlink =   | coauthors =   | title =The Theory of Quantized Fields I  | publisher = Physical Review, Volume 82  | date = 1951  | location =   | pages = 914  | url =   | doi = 10.1103/PhysRev.82.914  | id =   | isbn = }}</ref><ref>{{Cite book  | last = Schwinger  | first = Julian  | authorlink =   | coauthors =  | title =The Theory of Quantized Fields II | publisher = Physical Review, Volume 91  | date = 1953  | location =   | pages = 713  | url =   | doi = 10.1103/PhysRev.91.713  | id =   | isbn = }}
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This model exhibits [[colour confinement|confinement]] of the fermions and as such, is a toy model for [[Quantum_chromodynamics|QCD]]. A handwaving argument why this is so is because in two dimensions, classically, the potential between two charged particles goes linearly as <math>r</math>, instead of <math>1/r</math> in 4 dimensions (3 spatial 1 time).

==References== 
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[[Category:Quantum field theory]]
[[Category:Exactly solvable models]]

{{Quantum field theories}}