In quantum field theory, the Nambu–Jona-Lasinio model (or more precisely: the Nambu and Jona-Lasinio model) is a complicated effective theory of nucleons and mesons constructed from interacting Dirac fermions with chiral symmetry, paralleling the construction of Cooper pairs from electrons in the BCS theory of superconductivity. The "complicatedness" of the theory has become more natural as it is now seen as a low-energy approximation of the still more basic theory of quantum chromodynamics, which does not work perturbatively at low energies. Overview The model is much inspired by the different field of solid state theory, particularly from the BCS breakthrough of 1957. The first inventor of the Nambu–Jona-Lasinio model, Yoichiro Nambu, also contributed essentially to the theory of superconductivity, i.e., by the "Nambu formalism". The second inventor was Giovanni Jona-Lasinio. The common paper of the authors that introduced the model appeared in 1961. A subsequent paper included chiral symmetry breaking, isospin and strangeness. At the same time, the same model was independently considered by Soviet physicists Valentin Vaks and Anatoly Larkin. The model is quite technical, although based essentially on symmetry principles. It is an example of the importance of four-fermion interactions and is defined in a spacetime with an even number of dimensions. It is still important and is used primarily as an effective although not rigorous low energy substitute for quantum chromodynamics. The dynamical creation of a condensate from fermion interactions inspired many theories of the breaking of electroweak symmetry, such as technicolor and the top-quark condensate. Starting with the one-flavor case first, the Lagrangian density is The terms proportional to λ are the four-fermion interactions, which parallel the BCS theory. The global symmetry of the model is U(1)Q×U(1)χ where Q is the ordinary charge of the Dirac fermion and χ is the chiral charge. There is no bare mass term because of the chiral symmetry. However, there will be a chiral condensate (but no confinement) leading to an effective mass term and a spontaneous symmetry breaking of the chiral symmetry, but not the charge symmetry. With N flavors and the flavor indices represented by the Latin letters a, b, c, the Lagrangian density becomes Chiral symmetry forbids a bare mass term, but there may be chiral condensates. The global symmetry here is SU(N)L×SU(N)R× U(1)Q × U(1)χ where SU(N)L×SU(N)R acting upon the left-handed flavors and right-handed flavors respectively is the chiral symmetry (in other words, there is no