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Prog. Theor. Phys. Vol. 108 No. 3 (2002) pp. 571-590

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Non-Perturbative Renormalization Group Analysis in Quantum Mechanics

Ken-Ichi Aoki,* Atsushi Horikoshi,** Masaki Taniguchi*** and Haruhiko Terao****

Institute for Theoretical Physics, Kanazawa University, Kanazawa 920-1192, Japan

(Received June 24, 2002)

Abstract:

We analyze quantum mechanical systems using the non-perturbative renormalization group (NPRG). The NPRG method enables us to calculate quantum corrections systematically and is very effective for studying non-perturbative dynamics. We start with anharmonic oscillators and proceed to asymmetric double well potentials, supersymmetric quantum mechanics and many particle systems.


URL : http://ptp.ipap.jp/link?PTP/108/571/
DOI : 10.1143/PTP.108.571


*E-mail: aoki@hep.s.kanazawa-u.ac.jp
**E-mail: horikosi@hep.s.kanazawa-u.ac.jp
***E-mail: taniguti@snc.sony.co.jp
****E-mail: terao@hep.s.kanazawa-u.ac.jp

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References:

  1. K. G. Wilson and J. B. Kogut, Phys. Rep. 12 (1974), 75[CrossRef].
  2. K.-I. Aoki, Prog. Theor. Phys. Suppl. No. 131 (1998), 129[IPAP].
  3. T. R. Morris, Prog. Theor. Phys. Suppl. No. 131 (1998), 395[IPAP].
  4. D.-U. Jungnickel and C. Wetterich, Prog. Theor. Phys. Suppl. No. 131 (1998), 495[IPAP].
  5. The Exact Renormalization Group, Proceedings of the First Conference on the Exact Renormalization Group (World Scientific, Singapore, 1999).
  6. K.-I. Aoki, Int. J. Mod. Phys. B 14 (2000), 1249.
  7. C. Bagnuls and C. Bervillier, Phys. Rep. 348 (2001), 91[CrossRef].
  8. Proceedings of the Second Conference on the Exact Renormalization Group, Int. J. Mod. Phys. A 16 (2001).
  9. J. Berges, N. Tetradis and C. Wetterich, Phys. Rep. 363 (2002), 223[Elsevier].
  10. K.-I. Aoki, A. Horikoshi, M. Taniguchi and H. Terao, in The Exact Renormalization Group (World Scientific, Singapore, 1999), p. 194; hep-th/9812050[e-print arXiv].
  11. Large-Order Behaviour of Perturbation Theory, ed. J. C. Le Guillou and J. Zinn-Justin (North-Holland, 1990).
  12. S. Coleman, Aspects of symmetry (Cambridge University Press, 1985).
  13. H. Kleinert, Path Integrals in Quantum Mechanics Statistics and Polymer Physics (World Scientific, 1995).
  14. F. Wegner and A. Houghton, Phys. Rev. A 8 (1973), 401[APS].
  15. A. Hasenfratz and P. Hasenfratz, Nucl. Phys. B 270 (1986), 687[CrossRef].
  16. M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory (Addison-Wesley, 1995).
  17. K.-I. Aoki, K. Morikawa, W. Souma, J.-I. Sumi and H. Terao, Prog. Theor. Phys. 99 (1998), 451[IPAP].
  18. C. Wetterich, Phys. Lett. B 301 (1993), 90[CrossRef].
  19. B. Simon, Ann. Inst. Henri Poincare 38-3 (1983), 295; Ann. of Math. 120 (1984), 89; Ann. of Phys. 158 (1984), 415[CrossRef].
  20. P. Gosselin, B. Grosdidier and H. Mohrbach, Phys. Lett. A 256 (1999), 125[CrossRef].
  21. A. S. Kapoyannis and N. Tetradis, Phys. Lett. A 276 (2000), 225[CrossRef].
  22. T. R. Morris, Phys. Lett. B 329 (1994), 241[CrossRef].
  23. K.-I. Aoki and A. Horikoshi, unpublished.
  24. D. Zappala, Phys. Lett. A 290 (2001), 35[CrossRef].
  25. M. A. Martin-Delgado, G. Sierra and R. M. Noack, cond-mat/9903100[e-print arXiv].
  26. T. Kashiwa, Phys. Rev. D 59 (1999), 085002[APS].
  27. R. Guida, K. Konishi and H. Suzuki, Ann. of Phys. 241 (1995), 152[CrossRef]; ibid. 249 (1996), 109[CrossRef].
  28. T. Hatsuda, T. Kunihiro and T. Tanaka, Phys. Rev. Lett. 78 (1997), 3229[APS].
  29. T. Kunihiro, Prog. Theor. Phys. Suppl. No. 131 (1998), 459[IPAP]; Phys. Rev. D 57 (1998), 2035[APS].
  30. H. Aoyama, H. Kikuchi, T. Harano, I. Okouchi, M. Sato and S. Wada, Prog. Theor. Phys. Suppl. No. 127 (1997), 1[IPAP].
  31. H. Aoyama, H. Kikuchi, I. Okouchi, M. Sato and S. Wada, Phys. Lett. B 424 (1998), 93[CrossRef]; Nucl. Phys. B 553 (1999), 644[CrossRef].
  32. H. Aoyama, private communications.
  33. E. Witten, Nucl. Phys. B 188 (1981), 513[CrossRef]; ibid. 202 (1982), 253[CrossRef].
  34. P. Salomonson and J. W. van Holten, Nucl. Phys. B 196 (1982), 509[CrossRef].

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 119 No. 3 (2008) pp. 509-514 :
    A Finite-Range Scaling Method to Analyze Systems with Infinite-Range Interactions
    Ken-Ichi Aoki, Tamao Kobayashi and Hiroshi Tomita