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.
photon field strength,
is the gauge covariant derivative,
form the two-dimensional representation of the Clifford algebra.
A handwaving argument why this is so is because in two dimensions, classically, the potential between two charged particles goes linearly as
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.
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