## Equivalence of the four-Fermi theory with the [sigma]-model |

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### Contents

EQUIVALENCE OF THE FOURFERMI THEORY WITH | 10 |

CALLANSYMANZIK EQUATIONS AND THE OPERATOR | 34 |

CONCLUSION | 60 |

### Common terms and phrases

a-model ambiguity with regard BCS theory Bjorken boson regulator fields calculate Callan-Symanzik equations chain irreducible diagram chain-irreducible chiral SU(2)xSU(2 coefficients a^.(p compositeness condition condition relates constant g coupling constant Gq cut-off derive the Callan-Symanzik diagram of Figure diagrams shown divergence appearing divergent pieces Eguchi energy nQ(q Fermi fermion self energy Feynman rules finite four-Fermi interaction four-Fermi theory gap equation given by Eq Goldstone boson Goldstone mode governing the interactions Green's functions infinite number Lagrangian density Lagrangian is equivalent level of perturbation log a(l-a logarithmically divergent loop integral loop level mass shell matrix anomalous dimension matrix element momentum Nambu and Jona-Lasinio normal ground Nuovo Cimento orders of perturbation perturbation theory Phys point fermion loops quantities g quasi-particle excitations regularized provided renormalizable renormalization conditions renormalization group coefficients renormalized operators Section shown in Figure superconducting tend to infinity theory is equivalent Tung-Mow Yan vertex functions wave function renormalization Yukawa theory zero