A Strong Coupling Expansion for Fermion Field Theories and the Large $N$ Limit of the {Gross-Neveu} Model

An expansion in the fermion propagator is formulated for the N -species Gross-Neveu model in the large- N limit. Different regularisation schemes may be adopted and we compare two. We find that a continuum momentum cut-off is easiest to work with and automatically avoids spurious fermionic states which afflict a naive lattice formulation. Chiral symmetry is broken at zeroth order and the resulting expansion is inverse powers of g 2 N simplifies considerably for large N . In this limit the strong-coupling expansion may be summed to all orders. Extrapolation techniques, like Padé approximants, are not needed. Using a momentum cut-off we recover all the exact results previously derived by summing weak-coupling expansions.

QUANTUM CHROMODYNAMICS
FIELD THEORETICAL MODEL: GROSS-NEVEU
FIELD THEORY: SPINOR
SPINOR: FIELD THEORY
FERMION: PROPAGATOR
PERTURBATION THEORY: STRONG COUPLING
STRONG COUPLING: PERTURBATION THEORY
SYMMETRY BREAKING: CHIRAL
RENORMALIZATION: REGULARIZATION
INVARIANCE: U(N)

References(23)

Figures(0)

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A Strong Coupling Expansion for Fermion Field Theories and the Large NNN Limit of the {Gross-Neveu} Model

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A Strong Coupling Expansion for Fermion Field Theories and the Large $N$ Limit of the {Gross-Neveu} Model