Schwinger model
Encyclopedia
In physics, the Schwinger model, named after Julian Schwinger
, is the model describing 2D 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 instanton
s. 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.
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).
Julian Schwinger
Julian Seymour Schwinger was an American theoretical physicist. He is best known for his work on the theory of quantum electrodynamics, in particular for developing a relativistically invariant perturbation theory, and for renormalizing QED to one loop order.Schwinger is recognized as one of the...
, is the model describing 2D Euclidean
Euclidean
Euclidean relates to Euclid , a town or others. It may refer to:Geometry...
quantum electrodynamics
Quantum electrodynamics
Quantum electrodynamics is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved...
with a Dirac fermion. This model exhibits a spontaneous symmetry breaking
Spontaneous symmetry breaking
Spontaneous symmetry breaking is the process by which a system described in a theoretically symmetrical way ends up in an apparently asymmetric state....
of the U(1) symmetry due to a chiral condensate due to a pool of instanton
Instanton
An instanton is a notion appearing in theoretical and mathematical physics. Mathematically, a Yang–Mills instanton is a self-dual or anti-self-dual connection in a principal bundle over a four-dimensional Riemannian manifold that plays the role of physical space-time in non-abelian gauge theory...
s. The photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
in this model becomes a massive particle at low temperatures. This model can be solved exactly and is used as a toy model
Toy model
In physics, a toy model is a simplified set of objects and equations relating them that can nevertheless be used to understand a mechanism that is also useful in the full, non-simplified theory....
for other more complex theories.
This model exhibits confinement
Colour confinement
Color confinement, often simply called confinement, is the physics phenomenon that color charged particles cannot be isolated singularly, and therefore cannot be directly observed. Quarks, by default, clump together to form groups, or hadrons. The two types of hadrons are the mesons and the baryons...
of the fermions and as such, is a toy model for QCD
Quantum chromodynamics
In theoretical physics, quantum chromodynamics is a theory of the strong interaction , a fundamental force describing the interactions of the quarks and gluons making up hadrons . It is the study of the SU Yang–Mills theory of color-charged fermions...
. 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).