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In physics, the **Schwinger model**, named after Julian Schwinger, is the model^{[1]} describing 1+1D (1 spatial dimension + time) *Lorentzian* quantum electrodynamics which includes electrons, coupled to photons.

The model defines the usual QED Lagrangian

over a spacetime with one spatial dimension and one temporal dimension. Where is the photon field strength, is the gauge covariant derivative, is the fermion spinor, is the fermion mass and form the two-dimensional representation of the Clifford algebra.

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. This model also 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]}

**^**Schwinger, Julian (1962). "Gauge Invariance and Mass. II".*Physical Review*.**128**(5). Physical Review, Volume 128: 2425–2429. Bibcode:1962PhRv..128.2425S. doi:10.1103/PhysRev.128.2425.**^**Schwinger, Julian (1951). "The Theory of Quantized Fields I".*Physical Review*.**82**(6). Physical Review, Volume 82: 914–927. Bibcode:1951PhRv...82..914S. doi:10.1103/PhysRev.82.914. S2CID 121971249.**^**Schwinger, Julian (1953). "The Theory of Quantized Fields II".*Physical Review*.**91**(3). Physical Review, Volume 91: 713–728. Bibcode:1953PhRv...91..713S. doi:10.1103/PhysRev.91.713.