Reduction formula for Fermion loops and density correlations of the 1D Fermi gas

Journal of Statistical Physics

Volumn 96, Issue 3-4, 1999, Pages 613-626

  Neumayr, Arne ^a   Metzner, Walter ^a  

^a RWTH AACHEN UNIVERSITY   (Germany)

Author keywords

Density correlations; Fermi systems; Feynman amplitudes; Surface fluctuations

Indexed keywords

EID: 0033245978     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1004546206544     Document Type: Article

References (18)

1. 1. See, for example, V. N. Popov, Functional Integrals and Collective Excitations (Cambridge University Press, Cambridge, England, 1987).
2. 2. For a review, see W. Metzner, C. Castellani and C. Di Castro, Fermi systems with strong forward scattering, Adv. Phys. 47, No. 3 (1998).
3. 3. P. Kopietz, Bosonization of Interacting Fermions in Arbitrary Dimensions (Springer, 1997).
4. 4. V. L. Pokrovsky and A. L. Talapov, Ground state, spectrum, and phase diagram of two-dimensional incommensurate crystals, Phys. Rev. Lett. 42:65 (1979); The theory of two-dimensional incommensurate crystals, Sov. Phys. JETP 51:134 (1980).
5. 4. V. L. Pokrovsky and A. L. Talapov, Ground state, spectrum, and phase diagram of two-dimensional incommensurate crystals, Phys. Rev. Lett. 42:65 (1979); The theory of two-dimensional incommensurate crystals, Sov. Phys. JETP 51:134 (1980).
6. 5. For a review, see M. den Nijs, The domain wall theory of two-dimensional commensurate-incommensurate phase transitions, in Phase Transitions and Critical Phenomena, Vol. 12, C. Domb and J. L. Lebowitz, eds. (Academic Press, 1988).
7. 6. L. Balents and M. Kardar, Roughening of anisotropically reconstructed surfaces and the Hubbard model, Phys. Rev. B 46:16031 (1992), and references therein.
8. 7. See, for example, H. Fukuyama, Y. Hasegawa, and O. Narikiyo, Two-dimensional Hubbard model at low electron density, J. Phys. Soc. Japan 60:2013 (1991).
9. 8. J. Feldman, H. Knörrer, R. Sinclair, and E. Trubowitz, Evaluation of Fermion loops by higher residues, in Singularities, G. M. Greuel, ed. (Birkhauser, 1998).
10. 9. A. Neumayr and W. Metzner, Fermion loops, loop cancellation, and density correlations in two-dimensional Fermi systems, Phys. Rev. B 58:15449 (1998).
11. 10. P. Wagner, Evaluation of non-relativistic one-loop Feynman integrals by distributional methods, J. Math. Phys. 39:2436 (1998).
12. 11. A. L. Fetter and J. D. Walecka, Quantum Theory of Many-Particle Systems (McGraw-Hill, 1971).
13. 12. J. A. Hertz and M. A. Klenin, Fluctuations in itinerant-electron paramagnets, Phys. Rev. B 10:1084 (1974).
14. 13. For a comprehensive up-to-date review on one-dimensional Fermi systems, see J. Voit, One-dimensional Fermi liquids, Rep. Prog. Phys. 58:977 (1995).
15. 14. I. E. Dzyaloshinskii and A. I. Larkin, Correlation functions for a one-dimensional Fermi system with long-range interactions (Tomonaga model), Sov. Phys. JETP 38:202 (1974).
16. 15. F. D. M. Haldane, Luttinger liquid theory of one-dimensional quantum fluids: I. Properties of the Luttinger model and their extension to the general 1D interacting spinless Fermi gas, J. Phys. C 14:2585 (1981).
17. 16. M. Prähofer and H. Spohn, unpublished.
18. 17. N. Ortner and P. Wagner, On the evaluation of one-loop Feynman amplitudes in Euclidean quantum field theory, Ann. Inst. Henri Poicaré. Phys. Théor. 63:81 (1995).