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Schwinger model

From Wikipedia, the free encyclopedia

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 has a Lagrangian

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]


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

This page was last edited on 26 February 2021, at 19:55
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