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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).
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| ==References==
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| {{reflist}}
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| {{quantum-stub}}
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| [[Category:Quantum field theory]]
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| [[Category:Exactly solvable models]]
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| {{Quantum field theories}}
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Latest revision as of 01:29, 9 January 2015
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