Schwinger model

In physics, the Schwinger model, named after Julian Schwinger, is the model describing 2D 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.^[1]^[2]

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 $r$ , instead of $1/r$ in 4 dimensions (3 spatial 1 time).

References

^ Schwinger, Julian (1951). The Theory of Quantized Fields I. Physical Review, Volume 91. p. 914. {{cite book}}: Cite has empty unknown parameter: |coauthors= (help)
^ Schwinger, Julian (1953). The Theory of Quantized Fields II. Physical Review, Volume 91. p. 713. {{cite book}}: Cite has empty unknown parameter: |coauthors= (help)

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[1] Schwinger, Julian (1951). The Theory of Quantized Fields I. Physical Review, Volume 91. p. 914. {{cite book}}: Cite has empty unknown parameter: |coauthors= (help)

[2] Schwinger, Julian (1953). The Theory of Quantized Fields II. Physical Review, Volume 91. p. 713. {{cite book}}: Cite has empty unknown parameter: |coauthors= (help)

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