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Schwinger model

In today's article we are going to talk about Schwinger model, a topic that has gained great relevance in recent times. Schwinger model is a topic that arouses great interest and has a profound impact on today's society. Throughout this article, we will explore the different aspects related to Schwinger model, from its origin and history to its influence on the contemporary world. We will analyze its importance and the implications it has in various areas, as well as its possible repercussions in the future. We hope that this article will be a valuable source of information for all those interested in better understanding Schwinger model and its meaning today.

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In quantum field theory, the Schwinger model is a model describing 1+1D (time + 1 spatial dimension) quantum electrodynamics (QED) which includes electrons, coupled to photons. It is named after named after Julian Schwinger who developed it in 1962.[1]

The model defines the usual QED Lagrangian density

over a spacetime with one spatial dimension and one temporal dimension. Where is the photon field strength with symmetry group (unitary group), 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 quantum chromodynamics. 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]

References

  1. ^ 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.
  2. ^ 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.
  3. ^ 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.