Particle–Hole Ladders
A self contained analysis demonstrates that the sum of all particle-hole ladder contributions for a two dimensional, weakly coupled fermion gas with a strictly convex Fermi curve at temperature zero is bounded. This is used in our construction of two dimensional Fermi liquids. This summary article contains the statements of the main results. The proofs are contained in the full, electronic, article. Electronic Supplementary Material: Supplementary material is available in the online version of this article at http://dx.doi.org/10.1007/s00220-004-1038-2.
SINGLE SCALE ANALYSIS OF MANY FERMION SYSTEMS PART 3: SECTORIZED NORMS
The generic renormalization group map associated to a weakly coupled system of fermions at temperature zero is treated by supplementing the methods of Part 1. The interplay between position and momentum space is captured by "sectors". It is shown that the difference between the complete four-legged vertex and its "ladder" part is irrelevant for the sequence of renormalization group maps.
Renormalization group and the Fermi surface in the Luttinger model.
The exactly soluble Luttinger model can also be analyzed from the point of view of the renormalization group. A perturbation theory of the beta function of the model is derived. We argue that the main terms of the beta function vanish identically if the anomalous dimension is properly treated and if suitable properties of the exact solution are taken into account. Our treatment is purely perturbative and we do not discuss the problems of convergence of the formal series defining the beta function, it has recently been established, however, that the series defining it is convergent.