Schwinger model

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

References

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

Quantum field theories

Standard	Chern–Simons model Chiral model Kondo model Conformal field theory Local quantum field theory Noncommutative quantum field theory Non-linear sigma model Quartic interaction Quantum chromodynamics Quantum electrodynamics Quantum hadrodynamics Quantum Yang–Mills theory Schwinger model sine-Gordon Standard Model String theory Toda field theory Topological quantum field theory Wess–Zumino model Wess–Zumino–Witten model Yang–Mills theory Yang–Mills–Higgs model Yukawa model Thirring–Wess model

Four-fermion interactions	Thirring model Gross–Neveu model Nambu–Jona-Lasinio model

Related	History of quantum field theory Axiomatic quantum field theory Quantum field theory in curved spacetime

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