Abstract
Perturbation theory for the single-particle Green’s function of an interacting Fermi system usually works as long as the quasi-particle picture is valid.
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Chapter 1
T. Matsubara, Prog. Theor. Phys. 14, 35 (1955).
P. C. Martin and J. Schwinger, Phys. Rev. 115, 1342 (1959).
A. A. Abrikosov, L. P. Gorkov, and I. E. Dzyaloshinskii, Methods of Quantum Field Theory in Statistical Physics, (Dover, New York, 1963).
L. P. Kadanoff and G. Baym, Quantum Statistical Mechanics, (Benjamin, New York, 1962).
P. Nozières, Theory of Interacting Fermi Systems, (Benjamin, New York, 1964).
A. L. Fetter and J. D. Walecka, Quantum Theory of Many-Particle Systems, (McGraw-Hill, New York, 1971).
D. Pines and P. Nozières, The Theory of Quantum Liquids, (Addison-Wesley Advanced Book Classics, Redwood City, 1989).
L. D. Landau, Zh. Eksp. Teor. Fiz. 30, 1058 (1956) [Sov. Phys. JETP 3, 920 (1957)]; ibid. 32, 59 (1957) [Sov. Phys. JETP 5, 101 (1957)].
For an up-to-date review of Landau Fermi liquid theory see G. Baym and C. Pethick, Landau Fermi liquid theory, (Wiley, New York, 1991).
D. Vollhardt and P. Wölfle, The superfluid phases of Helium 3, (Taylor and Francis, London, 1990).
S. K. Ma, Modern Theory of Critical Phenomena, (Benjamin, Reading, 1976).
R. Shankar, Rev. Mod. Phys. 66, 129 (1994).
J. SĂłlyom, Adv. Phys. 28, 201 (1979).
V. J. Emery, in Highly Conducting One-Dimensional Solids, eds. J. T. Devreese, R. P. Evrard and V. E. van Doren, (Plenum, New York, 1979).
F. D. M. Haldane, J. Phys. C 14, 2585 (1981).
See, for example, F. H. L. Essler and V. E. Korepin, Exactly Solvable Models of Strongly Correlated Electrons, (World Scientific, Singapore, 1994).
S. Tomonaga, Prog. Theor. Phys. 5, 544 (1950).
J. M. Luttinger, J. Math. Phys. 4, 1154 (1963).
D. C. Mattis and E. H. Lieb, J. Math. Phys. 6, 304 (1965).
V. Meden and K. Schönhammer, Phys. Rev. B 46, 15753 (1992); K. Schönhammer and V. Meden, Phys. Rev. B 47, 16205 (1993).
J. Voit, Phys. Rev. B 47, 6740 (1993); Rep. Progr. Phys. 58, 977 (1995).
M. Stone, Bosonization, (World Scientific, Singapore, 1994).
P. W. Anderson, Phys. Rev. Lett. 64, 1839 (1990); 65, 2306 (1990); 66, 3226 (1991).
For a detailed discussion of the normal-state properties of the high-temperature superconductors see, for example, the articles by P. W. Anderson and Y. Ren, by B. Batlogg, and by P. A. Lee in High Temperature Superconductivity, edited by K. S. Bedell, D. E. Meltzer, D. Pines, and J. R. Schrieffer (Addison-Wesley, Reading, 1990). For more recent reviews see Physical Properties of High Temperature Superconductors IV, edited by D. M. Ginsberg (World Scientific, Singapore, 1994).
J. R. Engelbrecht and M. Randeria, Phys. Rev. Lett. 65, 1032 (1990); ibid. 66, 3325 (1991).
M. Fabrizio, A. Parola, and E. Tosatti, Phys. Rev. B 44, 1033 (1991).
D. Bohm and D. Pines, Phys. Rev. 92, 609 (1953).
D. Pines, The Many-Body Problem, (Benjamin, Reading, 1961).
A. Luther, Phys. Rev. B 19, 320 (1979).
F. D. M. Haldane, Helv. Phys. Acta. 65, 152 (1992); Luttinger’s Theorem and Bosonization of the Fermi surface, in Proceedings of the International School of Physics “Enrico Fermi”, Course 121, 1992, edited by R. Schrieffer and R. A. Broglia (North Holland, New York, 1994).
A. Houghton and J. B. Marston, Phys. Rev. B 48, 7790 (1993); A. Houghton, H.-J. Kwon, and J. B. Marston, Phys. Rev. B 50, 1351 (1994).
A. H. Castro Neto and E. Fradkin, Phys. Rev. Lett. 72, 1393 (1994); Phys. Rev. B 49, 10877 (1994).
A. Houghton, H.-J. Kwon, J. B. Marston, and R. Shankar, J. Phys. C 6, 4909 (1994); H.-J. Kwon, A. Houghton, and J. B. Marston, Phys. Rev. B 52, 8002 (1995).
A. H. Castro Neto and E. Fradkin, Phys. Rev. B 51, 4084 (1995).
P. Kopietz and K. Schönhammer, Bosonization of interacting fermions in arbitrary dimensions, Z. Phys. B 100, 259 (1996). This paper has originally been submitted on July 11, 1994 to Physical Review Letters.
P. Kopietz, J. Hermisson, and K. Schönhammer, Bosonization of interacting fermions in arbitrary dimensions beyond the Gaussian approximation, Phys. Rev. B 52, 10877 (1995).
P. Kopietz, Calculation of the single-particle Green’s function of interacting fermions in arbitrary dimension via functional bosonization, in the Proceedings of the Raymond L. Orbach Symposium, pages 101–119, edited by D. Hone (World Scientific, Singapore, 1996).
P. Kopietz and G. E. Castilla, Higher-dimensional bosonization with non-linear energy dispersion, Phys. Rev. Lett. 76, 4777 (1996).
J. Fröhlich, R. Götschmann, and P. A. Marchetti, J. Phys. A 28, 1169 (1995); J. Fröhlich and R. Götschmann, Bosonization of Fermi Liquids, preprint condmat/9606100, to appear in Phys. Rev. B.
T. Chen, J. Fröhlich and M. Seifert, Renormalization Group Methods: Landau-Fermi liquid and BCS Superconductors, in Fluctuating Geometries in Statistical Mechanics and Field Theory, edited by F. David and P. Ginsparg, (Elsevier, Amsterdam, 1996). This is part II of the lectures presented by J. Fröhlich at the 1994 Les Houches Summer School, session LXII (1994).
H. C. Fogedby, J. Phys. C 9, 3757 (1976).
D. K. K. Lee and Y. Chen, J. Phys. A 21, 4155 (1988).
J. Hermisson, Diplomarbeit, (Universität Göttingen, 1995, unpublished).
R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals, (McGraw-Hill, New York, 1965), chapter 9.
R. P. Feynman and F. L. Vernon, Ann. Phys. 24, 118 (1963).
D. Schmelzer, Phys. Rev. B 47, 11980 (1993); D. Schmelzer and A. Bishop, ibid. 50, 12733 (1994).
D. V. Khveshchenko, R. Hlubina, and T. M. Rice, Phys. Rev. B 48, 10766 (1994).
D. V. Khveshchenko, Phys. Rev. B 49, 16893 (1994); ibid. 52, 4833 (1995).
Y. M. Li, Phys. Rev. B 51, 13046 (1995).
C. Castellani, C. Di Castro, and W. Metzner, Phys. Rev. Lett. 72, 316 (1994).
C. Castellani and C. Di Castro, Physica C 235–240, 99 (1994).
W. Metzner, C. Castellani, and C. Di Castro, Fermi Systems with Strong Forward Scattering, to appear in Adv. Phys. (1997).
W. Kohn and J. M. Luttinger, Phys. Rev. 118, 41 (1960); J. M. Luttinger and J. C. Ward, ibid. 118, 1417 (1960).
W. Metzner and C. Castellani, Int. J. Mod. Phys. B 9, 1959 (1995).
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(1997). Introduction. In: Bosonization of Interacting Fermions in Arbitrary Dimensions. Lecture Notes in Physics Monographs, vol 48. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68495-4_1
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