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Part of the book series: CRM Series in Mathematical Physics ((CRM))

Abstract

After general comments on the relevance of field theory to condensed matter systems, the continuum description of interacting electrons in 1D is summarized. The bosonization procedure is then introduced heuristically, but the precise quantum equivalence between fermion and boson is also presented. Then the exact solution of the Tomonaga-Luttinger model is carried out. Two other applications of bosonization are then sketched. We end with a quick introduction to non-Abelian bosonization.

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10 References

  1. M. Stone, ed., Bosonization, World Scientific, Singapore, 1994, a collection of reprints.

    Google Scholar 

  2. I. Affleck, in Fields, Strings and Critical Phenomena, eds. E. Brézin and J. Zinn-Justin (Elsevier, Amsterdam, 1989), p. 564.

    Google Scholar 

  3. J. Cardy, Scaling and Renormalization in Statistical Physics, Cambridge Lecture Notes Phys. (Cambridge University Press, Cambridge, 1996). (See particularly Section 5.2 for a discussion of the perturbative Renormalization Group.)

    Google Scholar 

  4. A. Gogolin, A. Nersesyan, and A. Tsvelik, Bosonization and Strongly Correlated Systems (Cambridge University Press, Cambridge, 1998).

    Google Scholar 

  5. D. Allen and D. Sénéchal, Phys. Rev. B 55 (1997), 299.

    Article  ADS  Google Scholar 

  6. P. Ginsparg, Nuclear Phys. B 295 (1988), 153–170.

    Article  ADS  MathSciNet  Google Scholar 

  7. P.D. Francesco, P. Mathieu, and D. Sénéchal, Conformal Field Theory (Springer Verlag, New York, 1997). (See also the errata page at www.physique.usherb.ca/~dsenech/cft.htm.)

    MATH  Google Scholar 

  8. P. Ginsparg, in Fields, Strings and Critical Phenomena, eds. E. Brézin and J. Zinn-Justin (Elsevier, Amsterdam, 1989).

    Google Scholar 

  9. J. Kosterlitz and D. Thouless, J. Phys. C: Solid State Phys. 6 (1973), 1181.

    Article  ADS  Google Scholar 

  10. A. Luther and V. Emery, Phys. Rev. Lett. 33 (1974), 589.

    Article  ADS  Google Scholar 

  11. E. Witten, Comm. Math. Phys. 92 (1984), 455–472.

    Article  ADS  MATH  MathSciNet  Google Scholar 

  12. A. Zamolodchikov and V. Fateev, Sov. J. Nuclear Phys. 43 (1986), 657.

    Google Scholar 

  13. A. Tsvelik, Phys. Rev. B 42 (1990), 10499.

    Article  ADS  MathSciNet  Google Scholar 

  14. D. Shelton and D. Sénéchal, Phys. Rev. B 58 (1998), 6818.

    Article  ADS  Google Scholar 

  15. X.-G. Wen, Internat. J. Modern Phys. B 6 (1992), 1711–1762.

    Article  ADS  MathSciNet  Google Scholar 

  16. H. Schulz, G. Cuniberti, and P. Pieri, Fermi Liquids and Luttinger Liquids, Lecture Notes of the Chia Laguna (Italy), Summer School, September 1997, cond-mat/9807366.

    Google Scholar 

  17. C. Kane and M. Fisher, Phys. Rev. B 46 (1992), 1220.

    Article  Google Scholar 

  18. I. Affleck, Acta Phys. Polon. B 26 (1995), 1869, cond-mat/9512099.

    MATH  MathSciNet  Google Scholar 

  19. I. Affleck and F. Haldane, Phys. Rev. B 36 (1987), 5291.

    Article  ADS  MathSciNet  Google Scholar 

  20. M. Fabrizio, Phys. Rev. B 48 (1993), 15838.

    Article  ADS  Google Scholar 

  21. H. Schulz, Phys. Rev. B 53 (1996), R2959.

    Article  ADS  Google Scholar 

  22. H. Schulz, Phys. Rev. Lett. 64 (1990), 2831.

    Article  ADS  Google Scholar 

  23. N. Kawakami and S.-K. Yang, Prog. Theoret. Phys. 107 (1992), 59.

    Article  MathSciNet  ADS  Google Scholar 

  24. F. Haldane, in Perspectives in Many-Particle Physics, eds. R. Broglia and J.R. Schrieffer, (North Holland, Amsterdam 1994).

    Google Scholar 

  25. H.-J. Kwon, A. Houghton, and B. Marston, Phys. Rev. B 52 (1995), 8002.

    Article  ADS  Google Scholar 

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© 2004 Springer-Verlag New York, Inc.

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Sénéchal, D. (2004). An Introduction to Bosonization. In: Sénéchal, D., Tremblay, AM., Bourbonnais, C. (eds) Theoretical Methods for Strongly Correlated Electrons. CRM Series in Mathematical Physics. Springer, New York, NY. https://doi.org/10.1007/0-387-21717-7_4

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  • DOI: https://doi.org/10.1007/0-387-21717-7_4

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-00895-0

  • Online ISBN: 978-0-387-21717-8

  • eBook Packages: Springer Book Archive

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