Gross – Neveu Model
نویسنده
چکیده
for i = 1, · · · , N . Note that the sum over i is taken inside the parenthes before taking the square, which is not very clear in the way Peskin–Schroeder writes the Lagrangian density. I’ve put the subscript g0 to indicate that it is the bare coupling. This model describes massless spin 1/2 fermions in one spatial dimension with an attractive short-range potential. What the model does is that fermions get bound by the attractive force, and the fermion pair composite condenses to break a discrete Z2 symmetry. Because of the condensate, fermions acquire a mass. Therefore the dynamics is very similar to what actually happens in four-dimensional QCD (theory of strong interaction) or BCS (Bardeen–Cooper–Schrieffer) theory of superconductivity. Especially in the limit where N is large with g 0N fixed, this result is supposed to be exact. We will see why this is the case in the course of the problem.
منابع مشابه
Critical exponents of the Gross-Neveu model from the effective average action.
The phase transition of the Gross-Neveu model with N fermions is investigated by means of a nonperturbative evolution equation for the scale dependence of the effective average action. The critical exponents and scaling amplitudes are calculated for various values of N in d = 3. It is also explicitly verified that the Neveu-Yukawa model belongs to the same universality class as the Gross-Neveu ...
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