The Fermi Liquid Construction

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The following papers provide a mathematically rigorous construction of an interacting Fermi liquid at temperature zero in two space dimensions. It is a long and technical construction, spread over ten papers. We have written a brief guide [ html, pdf ] outlining the role that each of the papers plays in the construction. All of the papers have the authorship "J. Feldman, H. Knörrer, E. Trubowitz".

[ FKTf1] A Two Dimensional Fermi Liquid,
Part 1: Overview,
Commun. Math. Phys, 247 (2004) 1-47. (© Springer-Verlag)
[ FKTf2] A Two Dimensional Fermi Liquid,
Part 2: Convergence,
Commun. Math. Phys, 247 (2004) 49-111. (© Springer-Verlag)
[ FKTf3] A Two Dimensional Fermi Liquid,
Part 3: The Fermi Surface,
Commun. Math. Phys, 247 (2004) 113-177. (© Springer-Verlag)
[ FKTls] Particle-Hole Ladders, (summary version)
Commun. Math. Phys, 247 (2004) 179-194. (© Springer-Verlag)
[ FKTl] Particle-Hole Ladders, (full version)
Commun. Math. Phys, http://dx.doi.org/10.1007/s00220-004-1038-2. (© Springer-Verlag)
[ FKTo1] Single Scale Analysis of Many Fermion Systems,
Part 1: Insulators,
Rev. Math. Phys., 15 (2003) 949-994. (© World Scientific)
[ FKTo2] Single Scale Analysis of Many Fermion Systems,
Part 2: The First Scale,
Rev. Math. Phys., 15 (2003) 995-1038. (© World Scientific)
[ FKTo3] Single Scale Analysis of Many Fermion Systems,
Part 3: Sectorized Norms,
Rev. Math. Phys., 15 (2003) 1039-1120. (© World Scientific)
[ FKTo4] Single Scale Analysis of Many Fermion Systems,
Part 4: Sector Counting,
Rev. Math. Phys, 15 (2003) 1121-1169. (© World Scientific)
[ FKTr1] Convergence of Perturbation Expansions in Fermionic Models,
Part 1: Nonperturbative Bounds,
Commun. Math. Phys, 247 (2004) 195-242. (© Springer-Verlag)
[ FKTr2] Convergence of Perturbation Expansions in Fermionic Models,
Part 2: Overlapping Loops,
Commun. Math. Phys, 247 (2004) 243-319. (© Springer-Verlag)
[FKTa] Asymmetric Fermi Surfaces for Magnetic Schrödinger Operators,
Communications in Partial Differential Equations 25 (2000), 319-336.


The following papers give more pedagogical treatments of various aspects of the construction

Yellow Ball J.Feldman, H. Knörrer, D. Lehmann, E.Trubowitz:
Fermi liquids in two space dimensions, Paris 1994
in Construcive Physics. Results in Field Theory, Statistical Mechanics and Solid State Physics,
ed. V. Rivasseau, Springer Verlag (1995) 267-300.
postscript(516KB)

Yellow Ball J.Feldman, H. Knörrer, D. Lehmann, E.Trubowitz:
A Class of Fermi Liquids, Banff 1994
in ``Particles and Fields '94'', edited by G. Semenoff and L. Vinet, Springer 35-62 (1999).
postscript(393KB)

Yellow Ball J.Feldman:
Renormalization Group and Fermionic Functional Integrals, Aisenstadt Lectures 1999
[ pdf (768KB), typos]

Yellow Ball J.Feldman, H. Knörrer, E.Trubowitz:
Construction of a 2-d Fermi Liquid, Lisbon 2003.
Proceedings of the XIVth International Congress on Mathematical Physics, University of Lisbon, Portugal (ICMP2003) - © World Scientific.
pdf (198KB)


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