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Feldman, H. Kn¨orrer, E. Trubowitz We choose an arbitrary but fixed scale, j0 ≥ 2, and integrate the first scales, between 1 and j0 , in one fell swoop. 8. There are (M and j0 –dependent) constants µ, λ¯ and β0 such that, for all 1 λ < λ¯ and β0 ≤ β ≤ λυ/5 , the following holds: Let X ∈ Nd+1 with X0 < µ, δe ∈ E with δ eˆ 1,∞ ≤ X and V(ψ) = B4 dξ1 ···dξ4 V (ξ1 ,··· ,ξ4 ) ψ(ξ1 ) · · · ψ(ξ1 ) with an antisymmetric function V fulfilling V 1,∞ ≤ λ e0 (X). Write ˜ (≤j ) C−δe0 (≤j ) V (ψ) (φ, ψ) = V(ψ) + 21 φJ C−δe0 J φ + m,n≥0 m+n even Bm+n dη1 ···dηm dξ1 ···dξn Wm,n (η1 ,··· ,ηm ,ξ1 ,··· ,ξn ; δe) ×φ (η1 ) · · · φ (ηm ) ψ (ξ1 ) · · · ψ(ξn ) with kernels Wm,n that are separately antisymmetric under permutations of their η and ξ arguments.

Physics Notes, Vol. : Number of Feynman Diagrams and Convergence. , Magnen, J. : Interacting Fermi liquid in three dimensions at finite temperature: Part I: Convergent Contributions. Ann. : Interacting Fermi liquid in two dimensions at finite temperature. Part I: Convergent Attributions. Commun. Math. Phys. : Interacting Fermi liquid in two dimensions at finite temperature. Part II: Renormalization. Commun. Math. Phys. : Fermi Liquids in Two-Space Dimensions. In: Constructive Physics, V. , Springer Lecture Notes in Physics 446, Berlin-Heidelberg-New York: Springer Verlag, 1995, pp.

Ladders . . . . . . . . . . . . . . . Infrared Limit of Finite Scale Green’s Functions . . . . One Recursion Step . . . . . . . . . . . . 1. Input and Output Data . . . . . . . . . . 2. Integrating Out a Scale . . . . . . . . . . 3. Sector Refinement, ReWick Ordering and Renormalization X. The Recursive Construction of the Green’s Functions . . . 1. Initialization at j = j0 . . . . . . . . . . 2. Recursive Step j → j + 1 . .

### Communications in Mathematical Physics - Volume 247 by M. Aizenman (Chief Editor)

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