Gross-Neveu model

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The Gross-Neveu model is a field theory with Lagrangian

\mathcal{L}=\bar{\psi}_a \left(i\partial\!\!\!/-m \right) \psi^a + \frac{g^2}{2}\left(\bar{\psi}_a \psi^a\right)^2.

Here \psi^a\, is an N\,-component massless Dirac fermion. This theory is renormalizable and asysmptotically free in 2 dimensions.

Contents

Auxiliary field

Large N

Discrete chiral symmetry breaking

References

[1] [2] [3] [4] [5]

  1. ↑ Gross, David J. and Neveu, André (1974). "Dynamical symmetry breaking in asymptotically free field theories". Phys. Rev. D 10: 3235--3253. DOI:10.1103/PhysRevD.10.3235. 
  2. ↑ Witten, Edward (1978). "Chiral Symmetry, the 1/N Expansion, and the SU(N) Thirring model". Nucl. Phys. B145: 110. DOI:10.1016/0550-3213(78)90416-9. 
  3. ↑ Zinn-Justin, Jean (2000). "Quantum field theory at finite temperature: An introduction". arXiv:hep-ph/0005272. 
  4. ↑ Zinn-Justin, Jean (1991). "Four fermion interaction near four-dimensions". Nucl. Phys. B367: 105-122. DOI:10.1016/0550-3213(91)90043-w. 
  5. ↑ Rosenstein, Baruch; Warr, Brian J.; Park, Seon H. (1989). "The Four Fermi Theory Is Renormalizable in (2+1)- Dimensions". Phys. Rev. Lett. 62: 1433-1436. DOI:10.1103/PhysRevLett.62.1433. 
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