\begin{thebibliography}{99}
\addcontentsline{toc}{chapter}{Bibliographie}

\bibitem{Hubbard57}               
  \bibart{J.~Hubbard}{Proc.~Roy.~Soc. Ser. A}{240}{539}{1957}; 
  \bibartibid{Proc.~Roy.~Soc. Ser. A}{243}{336}{1958}.
  \comment{Hubbard (citations from Voit[82] and Florian[2.19-21])}
\bibitem{Mott}
  \bibbook{N.F.~Mott}{Metal-Insulator Transitions}{Taylor and Francis,
  London, 2nd. edition}{1990}.
\bibitem{Florian}
  \bibbook{F.~Gebhard}{The Mott Metal Insulator Transition}
  {Springer Tracts in Modern Physics, Vol.~137}{1997}.
\bibitem{McWhan69}
  \bibart{D.B.~McWhan, T.M.~Rice, J.P.~Remeika}
  {Phys. Rev. Lett.}{23}{1384}{1969};
  \bibart{D.B.~McWhan, J.P.~Remeika, T.M.~Rice, W.F.~Brinkman, 
    J.P.~Maita, A.~Menth}{Phys. Rev. Lett.}{27}{941}{1971}; 
  \bibart{D.B.~McWhan, A.~Menth, J.P.~Remeika, W.F.~Brinkman, T.M.~Rice}
  {Phys. Rev. B}{7}{1920}{1973}.
\bibitem{V2O3model}
  \bibart{K.I.~Kugel, D.I.~Khomskii}{Sov. Phys. JETP}{37}{725}{1973};
  \bibart{C.~Castellani, C.R.~Natoli, J.~Ranninger}
  {Phys. Rev. B}{18}{4945, 4967, 5001}{1978};
  \bibart{L.~Roth}{Phys.~Rev}{149}{306}{1966};
  \bibart{H.~Capellmann}{Phys. Rev. B}{7}{4153}{1973};
  \bibart{M.~Cyrot, C.~Lyon-Caen}{J. Phys. C}{6}{L274}{1975};
  voir aussi r\'ef.~\cite[chap.~2.4.2]{Florian}.
\bibitem{BednorzMueller86}
  \bibart{J.G.~Bednorz, K.A.~M\"uller}{Z. Phys. B}{64}{189}{1986}.
\bibitem{Goebel}
  \bibbook{H.~G\"obel}
  {Etude des corr\'elations \'electroniques dans la limte du couplage
    fort et application aux supraconducteurs \`a oxyde de cuivre}
  {Th\`ese, Universit\'e Joseph Fourier, Grenoble}{1993}.
\bibitem{Emery87}
  \bibart{V.J.~Emery}{Phys. Rev. Lett.}{58}{2794}{1987}.
\bibitem{Catherine}
  \bibbook{C.~P\'epin}
  {Ph\'enom\`enes critiques autour de la transition magn\'etique dans
    les Fermions Lourds}
  {Th\`ese, Universit\'e Joseph Fourier, Grenoble}{1996}.
\bibitem{LiebWu}
  \bibart{E.H.~Lieb, F.Y. Wu}{Phys. Rev. Lett.}{20}{1445}{1968}.
  \comment{Bethe ansatz original}
\bibitem{Blaizot}
  \bibbook{J.P.~Blaizot, G.~Ripka}
  {Quantum Theory of Finite Systems, The MIT Press, Cambridge}{1986}.  
\bibitem{Rowe}
  \bibart{D.J.~Rowe}{Rev. Mod. Phys.}{40}{153}{1968}.
\bibitem{Roth69}
  \bibart{L.M.~Roth}{Rhys. Rev.}{184}{451}{1969}.
\bibitem{Schuck71}
  \bibart{P.~Schuck}{Z. Phys}{241}{395}{1971}.
\bibitem{Dukelsky90}
  \bibart{J.~Dukelsky, P.~Schuck}{Nucl. Phys. A}{512}{466}{1990};
  \bibart{J.~Dukelsky, P.~Schuck}{Mod. Phys. Lett. A}{26}{2429}{1991}.
\bibitem{Roepke94}
  \bibart{G.~R\"opke}{Ann. Physik (Leipzig)}{3}{145}{1994};
  \bibart{G.~R\"opke}{Z. Phys. B.}{99}{83}{1995}.
\bibitem{Dukelsky96}
  \bibart{J.~Dukelsky, P.~Schuck}{Phys. Lett. B}{387}{233}{1996}.
\bibitem{DRS98}
  \bibart{J.~Dukelsky, G.~R\"opke, P.~Schuck}{Nucl. Phys. A}{628}{17}{1998}.
\bibitem{Thierry}
  \bibbook{T.~Bertrand}{L'approximation des phases al\'eatoires
    autocoh\'erente appliqu\'ee \`a un mod\`ele sch\'ematique de la
    th\'eorie des champs}
  {Th\`ese, Universit\'e Claude Bernard, Lyon}{1998}.
\bibitem{Krueger}
  \bibart{P.~Kr\"uger, P.~Schuck}{Europhys. Lett.}{27}{395}{1994}.
\bibitem{Beenen95}
  \bibart{J.~Beenen, D.M.~Edwards}{Phys. Rev. B}{52}{13\,636}{1995}.
  \comment{SCRPA for attractive Hubbard Model and single-particle propagator}
\bibitem{Kuzemsky91}
  \bibart{A.L.~Kuzemsky}{Phys. Lett. A}{153}{466}{1991}.
  \comment{SCRPA-like theory in single-impurity Anderson model (1pGF)}
\bibitem{Kuzemsky93}
  \bibart{A.L.~Kuzemsky, J.C.~Parlebas, H.~Beck}{Physica A}{198}{606}{1993};
  \bibart{A.L.~Kuzemsky}{Il Nuovo Cimento}{109 B}{829}{1994}.
  \comment{SCRPA-like theory in Hubbard model (1pGF)}
\bibitem{Migdal57}
  \bibart{A.B.~Migdal}{Sov. Phys. JETP}{5}{333}{1957}.
\bibitem{Luttinger60}
  \bibart{J.M.~Luttinger, J.C.~Ward}{Phys. Rev.}{118}{1417}{1960};
  \bibart{J.M.~Luttinger}{Phys. Rev.}{119}{1153}{1960}; 
  \bibartibid{Phys. Rev.}{121}{942}{1961}.
  \comment{Migdal57, Luttinger60:
    Luttinger theorem (citation from Florian [1.88])}
\bibitem{Nozieres}
  \bibbook{P.~Nozi\`eres}{Le probl\`eme \`a N corps}{Dunod, Paris}{1963}.
\bibitem{NozieresPines}
  \bibbook{P.~Nozi\`eres, D.~Pines}
  {The Theory of Quantum Liquids: Normal Fermi Liquids}
  {Addison-Wesley}{1989}.       % first edition 1966
\bibitem{FetterWalecka}
  \bibbook{A.L.~Fetter, J.D.~Walecka}
  {Quantum Theory of Many-Particle Systems}{Mc\-Graw-Hill, Inc.}{1971}.
\bibitem{Nolting}
  \bibbook{W.~Nolting}
  {Grund\-kurs Theo\-re\-tische Phy\-sik, 7.~Viel--Teil\-chen--Theo\-rie} 
  {Zim\-mer\-mann--Neu\-fang}{1992}.
\bibitem{Orland}  
  \bibbook{J.W.~Negele, H.~Orland}
  {Quantum Many--Particle Systems}{Addison--Wesley}{1988}.  
\bibitem{Jackson}
  \bibbook{J.D.~Jackson}{Classical Electrodynamics}
  {John Wiley \& Sons, Second Edition, New York}{1975}.
\bibitem{BCS}
  \bibart{J.~Bardeen, L.N.~Cooper, J.R.~Schrieffer}
  {Phys. Rev.}{108}{1175}{1957}.
\bibitem{RS}      
  \bibbook{P.~Ring, P.~Schuck}
  {The Nuclear Many--Body Problem}{Springer, Berlin}{1980}. 
\bibitem{Nozieres58}
  \bibart{P.~Nozi\`eres, D.~Pines}{Phys. Rev}{109}{741}{1958}.
\bibitem{Kubo}
  \bibart{R.~Kubo}{Jour. Phys. Soc. Japan}{17}{1100}{1962}.
\bibitem{Schuck73}
  \bibart{P.~Schuck, S.~Ethofer}{Nucl. Phys. A}{212}{269}{1973}. 
\bibitem{Baranger}
  \bibart{M.~Baranger}{Nucl. Phys. A}{149}{225}{1970}. 
\bibitem{Weigel}
  \bibart{M.K.~Weigel, J.~Winter}{J. Phys. G: Nucl. Phys.}{4}{1427}{1978}.
\bibitem{EthoferSchuck}
  \bibart{S.~Ethofer, P.~Schuck}{Z. Phys}{228}{264}{1969}.
\bibitem{Randeria}              
  \bibart{L.~Belkhir, M.~Randeria}{Phys. Rev. B}{49}{6829}{1994}.
  \comment{Crossover from Cooper pairs to composite bosons: 
    A generalized RPA analysis of collective excitations}
\bibitem{Hubbard63}               
  \bibart{J.~Hubbard}{Proc.~Roy.~Soc. Ser. A}{276}{238}{1963}; 
  \bibartibid{Proc.~Roy.~Soc. Ser. A}{277}{237}{1963}.
\bibitem{Hubbard64}
  \bibart{J.~Hubbard}{Proc.~Roy.~Soc. Ser. A}{281}{401}{1964}.
\bibitem{Anderson59}
  \bibart{P.W.~Anderson}{Phys. Rev.}{115}{2}{1959}.
\bibitem{Fulde}
  \bibbook{P.~Fulde}{Electron Correlations in Molecules and Solids}
  {Springer Series in Solid-State Sciences {\bf 100}, Berlin}{1991}.
\bibitem{Auerbach}
  \bibbook{A.~Auerbach}{Interacting Electrons and Quantum Magnetism}
  {Springer}{1994}.
\bibitem{ElkGasser}
  \bibbook{K.~Elk, W.~Gasser}
  {Die Methode der Greenschen Funktionen in der Festk\"orperphysik}
  {Akademie-Verlag, Berlin}{1979}.
\bibitem{White}
  \bibbook{R.M.~White}{Quantum Theory of Magnetism}
  {Springer-Verlag, Berlin, 2nd. and updated edition}{1983}.
\bibitem{Gutzwiller}
  \bibart{M.C.~Gutzwiller}{Phys. Rev. Lett.}{10}{156}{1963}; 
  \bibartibid{Phys. Rev.}{134}{A923}{1964}; 
  \bibartibid{Phys. Rev.}{137}{A1726}{1965}.
  \comment{ Florian [3.68,3.69] }
\bibitem{Stratonovich}
  \bibart{R.L.~Stratonovich}{Sov. Phys. Dokl.}{2}{416}{1957};\\
  pour un r\'esum\'e voir r\'ef.~\cite{Florian,Orland}.
\bibitem{Lavagna}
  \bibart{M.~Lavagna}{Phys. Rev. B}{41}{142}{1990};
  {\em ibid.} in \bibcomp{The Hubbard Model -- Recent Results}
  {M.~Rasetti}{World Scientific, Singapore}{1991}.
\bibitem{Kotliar86}
  \bibart{G.~Kotliar, A.E.~Ruckenstein}{Phys. Rev. Lett.}{57}{1362}{1986}. 
\bibitem{Penn65}
  \bibart{D.R.~Penn}{Phys. Rev.}{142}{350}{1966}.
\bibitem{Stoner}
  \bibart{E.C.~Stoner}{Journal de Phys. et Rad.}{12}{372}{1951}.
\bibitem{Cyrot}
  \bibart{M.~Cyrot}{Physica B}{91}{141}{1977}.
\bibitem{Brinkman}
  \bibart{W.F.~Brinkman, T.M.~Rice}{Phys. Rev. B}{2}{1324}{1970}.
\bibitem{MerminWagner}
  \bibart{N.D.~Mermin, H.~Wagner}{Phys. Rev. Lett.}{17}{1133}{1966}.
\bibitem{Haemmerlin}
  \bibbook{G.~H\"ammerlin, K.-H.~Hoffmann}
  {Numerische Mathematik}{Springer, Berlin, 2.~Auf\/lage}{1991}.
\bibitem{NR}
  \bibbook{W.H.~Press, B.P.~Flannery, S.A.~Teukolsky, W.T.~Vetterling}
  {Numerical Recipes in C}{Cambridge University Press, New York}{1988}.
\bibitem{Thouless}
  \bibart{D.J.~Thouless}{Nucl.~Phys.}{22}{78}{1961}.
  \comment{Thouless from RS}
\bibitem{Vilk94}
  \bibart{Y.M. Vilk, L.~Chen, A.-M.S.~Tremblay}
  {Phys. Rev. B}{49}{13\,267}{1994};  
  \bibartibid{Physica C}{235-240}{2235}{1994}.
  \comment{citations from preprint}
\bibitem{Vilk96}
  \bibart{Y.M.~Vilk, A.-M.S.~Tremblay}{Europhys. Lett.}{33}{159-164}{1996}.
  \comment{part from ``New many-body approach to the Hubbard model
    and single partice pseudogap}
\bibitem{Vilk97}
  \bibart{Y.M.~Vilk, A.-M.S.~Tremblay}{J. Phys. I France}{7}{1309-1368}{1997}.
\bibitem{Mahan}
  \bibbook{G.D.~Mahan}
  {Many-Particle Physics}{Plenum Press, New York}{1981}.
\bibitem{Gross}
  \bibbook{E.K.U.~Gross, E.~Runge, O.~Heinonen}
  {Many-Particle Theory}{IOP Publishing}{1991}.
\bibitem{Schulz97}
  \bibbook{H.J.~Schulz, G.~Cuniberti, P.~Pieri}
  {Fermi Liquids and Luttinger Liquids}
  {Lecture Notes of the Chia Laguna (Italy) Summer School (cond-mat/9807366v2)}
  {1997}.
\bibitem{Voit}
  \bibart{J.~Voit}{Reports on Progress in Physics}{58}{977}{1995}.
\bibitem{Roth}
  \bibbook{S.~Roth}{One-Dimensional Metals}
  {VCH Verlagsgesellschaft, Weinheim}{1995}.
\bibitem{Tomonaga50} 
  \bibart{S.~Tomonaga}{Prog. Theor. Phys.}{5}{544}{1950}.
\bibitem{Luttinger63} 
  \bibart{J.M.~Luttinger}{J. Math. Phys.}{4}{1154}{1963}.
\bibitem{MattisLieb65}
  \bibart{D.C.~Mattis, E.H.~Lieb}{J. Math. Phys.}{6}{304}{1965}.
\bibitem{Voit95}
  J.~Voit in 
  \bibcomp{The Hubbard Model: Its Physics and Mathematical Physics}
  {D.~Baeriswyl, D.K.~Campbell, J.M.P.~Carmelo, F.~Guinea, and E.~Louis}
  {NATO ASI Series B {\bf 343}, p263-272, Plenum Press, New York}{1995}.
\bibitem{Voit98}
  J.~Voit in 
  \bibcomp{Proceedings of the Ninth International Conference on Recent
    Progress in Many-Body Theories (Sydney)} 
  {D.~Neilson}{World Scientific}{1998}.
\bibitem{Mattis}
  \bibcomp{The Many-Body Problem, An Encyclopedia of Exactly Solved
    Models in One Dimension}{D.C.~Mattis}
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\bibitem{KorepinEssler}
  \bibcomp{Exactly Solvable Models of Strongly Correlated Electrons}
  {V.E.~Korepin and F.H.L E\ss{}ler}{World Scientific, Singapore}{1995}.
\bibitem{Andrei}
  N.~Andrei ``{\em Integrable Models in Condensed Matter Physics}, p457, in  
  \bibcomp{Low-Dimensional Quantum Field Theories for Condensed Matter
    Physicists}{S,~Lundquist, G.~Morandi, and Yu Lu}
  {Series on Modern Condensed Matter Physics {\bf 6},
    World Scientific, Singapore (cond-mat/9408101)}{1995}.
  \comment{Chapter 4, The Hubbard Model by Andres Jerez}
\bibitem{Korepin}
  \bibbook{V.E.~Korepin, A.G.~Izergin, N.M.~Bogoliubov}
  {Quantum Inverse Scattering Method and Correlation Functions} 
  {Cambridge University Press, New York}{1993}.
\bibitem{CarmeloBaeriswyl}
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\bibitem{Kluemper90}
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\bibitem{Schadschneider91}
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\bibitem{Kluemper96}
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\bibitem{Kirchner98}
  S.~Kirchner, H.G.~Evertz, W.~Hanke, cond-mat/9804148 (1998).
\bibitem{Schulz98}
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\bibitem{Florian92}
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\bibitem{Florian94}
  \bibart{F.~Gebhard, A.~Grindt, A.E.~Ruckenstein}
  {Phys. Rev. B}{49}{10\,926}{1994}.
\bibitem{Sorella88}
  \bibart{S.~Sorella, E.~Tosatti, S.~Baroni, R.~Car, M.~Parinello}
  {Int. J. Mod. Phys. B}{1}{993}{1988}. 
  \comment{QMC in half filled HM, citation [114] from Voit} 
\bibitem{Sorella90}
  \bibart{S.~Sorella, A.~Parola, M.~Parinello, E.~Tosatti}
  {Europhys. Lett.}{12}{721}{1990}.
\bibitem{BaeriswylLinden}
  D.~Baeriswyl, W.~von der Linden 
  in \bibcomp{The Hubbard Model -- Recent Results}
  {M.~Rasetti}{World Scientific, Singapore}{1991}.  
\bibitem{Dzierzawa}
  M.~Dzierzawa in 
  \bibcomp{The Hubbard Model: Its Physics and Mathematical Physics}
  {D.~Baeriswyl, D.K.~Campbell, J.M.P.~Carmelo, F.~Guinea, and E.~Louis}
  {NATO ASI Series B {\bf 343}, p327, Plenum Press, New York}{1995}.
  \comment{QMC in quarter filled HM}
% Bethe ansatz
\bibitem{OgataShiba89}
  M.~Ogata, H.~Shiba in {\em Technical Report of ISSP}, published by
  The Institute of Solid State Physics, The University of Tokyo,
  Ser.~A, No.~2189, (1989).
\bibitem{OgataShiba90}
  \bibart{M.~Ogata, H.~Shiba}{Phys. Rev. B}{41}{2326}{1990};
  \bibart{H.~Shiba, M.~Ogata}{Journ. of Magnetism and Magnetic Materials}
  {90 \& 91}{205-209}{1990};
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\bibitem{Penc95}
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\bibitem{Parola90}
  \bibart{A.~Parola, S.~Sorella}{Phys. Rev. Lett}{64}{1831}{1990}.
  \comment{Asymptotic Spin-Spin Correlations of the $U\to\intfy$
    one-dimensional Hubbard Model}
\bibitem{Preuss94}
  \bibart{R.~Preuss, A.~Muramatsu, W.~von der Linden, F.F.~Assad, W.~Hanke}
  {Phys. Rev. Lett}{73}{732}{1994}.
  \comment{Spectral properties of the one-dimensional Hubbard model}
\bibitem{Kittel}
  \bibbook{C.~Kittel}{Quantum Theory of Solids}{John Wiley \& Sons}{1987}.
\bibitem{BaeriswylCarmeloLuther}
  \bibart{D.~Baeriswyl, J.~Carmelo, A.~Luther}{Phys. Rev. B}{33}{7247}{1986}; 
  \bibarterr{Phys. Rev. B}{34}{8976(E)}{1986}.
\bibitem{Schoenhammer95}
  \bibart{K.~Sch\"onhammer, O.~Gunnarsson, R.M.~Noack}
  {Phys. Rev. B}{52}{2504}{1995}.
  \comment{Fig. 4.1. from Florian}
\bibitem{Toivanen}
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\bibitem{Georges96}
  \bibart{A.~Georges, G.~Kotliar, W.~Krauth, M.~Rozenberg}
  {Rev. Mod. Phys.}{68}{13}{1996}.
\bibitem{LoganNozieres}
  \bibart{D.E.~Logan, P.~Nozi\`eres}
  {Phil. Trans. Roy. Soc. London A}{356}{249}{1998}.
  \comment{``The Mott Transition''}
\bibitem{Tusch}
  \bibbook{M.A.~Tusch}
  {Interplay between disorder and electron interactions: 
    theoretical studies of an Anderson-Hubbard model} 
  {Th\`ese, University of Oxford, Michelmas}{1993}.
\bibitem{Migdal}
  \bibbook{A.B.~Migdal}
  {Theory of Finite Fermi Systems and Applications to Atomic Nuclei}
  {Monographs and Texts in Physics and Astronomy, Interscience Publishers, 
    a division of John Wiley \& Sons, New York}{1967}.
\bibitem{Vollhardt93}
  D.~Vollhardt in 
  \bibcomp{Correlated Electron Systems, Vol. {\bf 9}}
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\bibitem{MuellerH89}
  \bibart{E.~M\"uller-Hartmann}{Int. J. Mod. Phys. B}{3}{2169}{1989}.
\bibitem{Dongen89}
  \bibart{P.G.-J.~van Dongen, F.~Gebhard, D.~Vollhardt}
  {Z. Phys. B}{76}{199}{1989}.
\bibitem{Logan96} 
  \bibart{D.E.~Logan, M.P.~Eastwood, M.A.~Tusch}
  {Phys. Rev. Lett.}{76}{4785}{1996};
  \bibartibid{J.Phys.: Condens. Matter}{9}{9621-9638}{1997}.
\bibitem{Logan98} 
  \bibart{D.E.~Logan, M.P.~Eastwood, M.A.~Tusch}
  {J.Phys.: Condens. Matter}{10}{2673-2700}{1998}. 
% ==================================================
% appendix
% ==================================================
\bibitem{Mattuck}
  \bibbook{R.D.~Mattuck}
  {A Guide to feynman Diagrams in the Many-Body Problem} 
  {Dover Publications, New York, 2nd. edition}{1976}.
\bibitem{Benard}
  \bibart{P.~B\'enard, L.~Chen, A.-M.S.~Tremblay}
  {Phys. Rev. B}{47}{15\,217}{1993}. 
\bibitem{Schaefer98}
  S.~Sch\"afer, P.~Schuck, cond-mat/9804011, 
  to be published in Phys. Rev. B. (1998).
\end{thebibliography}