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Prog. Theor. Phys. Vol. 124 No. 5 (2010) pp. 731-746

[ Full Text PDF : FREE ACCESS (249K) ]

Invited Papers

Spontaneous Symmetry Breaking

— Variations on a Theme —

Giovanni Jona-Lasinio1,2

1Dipartimento di Fisica, “Sapienza”, Università di Roma, Piazzale A. Moro 2, Roma 00185, Italy
2Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1, Roma 00185, Italy

(Received August 7, 2010; Revised September 29, 2010)

Abstract:

Spontaneous symmetry breaking (SSB) is a widespread phenomenon in several areas of physics. In this paper I wish to illustrate some situations where spontaneous symmetry breaking presents non obvious aspects. The first example is taken from molecular physics and is related to the paradox of existence of chiral molecules. The second case refers to a Dirac field in presence of a magnetic field. Gusynin, Miransky and Shovkovy have shown that Nambu–Jona-Lasinio (NJL) models, where SSB of chiral symmetry takes place for the nonlinear coupling over a certain threshold, in presence of a magnetic field exhibit SSB for any value of the coupling. They called this phenomenon magnetic catalysis. I will discuss this problem in 2 + 1 dimensions from an operatorial point of view and show that the basic phenomenon is a double pairing induced by the magnetic field in the vacuum for any value of the mass. This pairing provides the environment responsible for chiral symmetry breaking in NJL models with very weak nonlinearities. The third case illustrates briefly SSB in stationary nonequilibrium states and its possible relevance in natural phenomena.

Subject Index : 013, 057, 062, 063, 130
URL : http://ptp.ipap.jp/link?PTP/124/731/
DOI : 10.1143/PTP.124.731

[ Full Text PDF : FREE ACCESS (249K) ] Citation:

References:

  1. F. Hund, Z. Phys. 43 (1927), 805.
  2. P. Claverie and G. Jona-Lasinio, Phys. Rev. A 33 (1986), 2245[APS].
  3. G. Jona-Lasinio, C. Presilla and C. Toninelli, Phys. Rev. Lett. 88 (2002), 123001[APS].
  4. V. P. Gusynin, V. A. Miransky and I. A. Shovkovy, Phys. Rev. D 52 (1995), 4718[APS].
  5. V. P. Gusynin, V. A. Miransky and I. A. Shovkovy, Nucl. Phys. B 462 (1996), 249[CrossRef].
  6. Y. Nambu and G. Jona-Lasinio, Phys. Rev. 122 (1961), 345[APS].
  7. G. Jona-Lasinio and F. M. Marchetti, Phys. Lett. B 459 (1999), 208[CrossRef].
  8. M. R. Evans, D. P. Foster, C. Godrèche and D. Mukamel, Phys. Rev. Lett. 74 (1995), 208[APS].
  9. V. Popkov, M. R. Evans and D. Mukamel, J. of Phys. A 41 (2008), 432002[CrossRef].
  10. S. Gupta, D. Mukamel and G. M. Schütz, J. of Phys. A 42 (2009), 485002[CrossRef].
  11. M. Simonius, Phys. Rev. Lett. 40 (1978), 980[APS].
  12. R. A. Harris and L. Stodolsky, J. Chem. Phys. 74 (1981), 2145[CrossRef].
  13. J. Trost and K. Hornberger, Phys. Rev. Lett. 103 (2009), 023202[APS].
  14. G. Jona-Lasinio, F. Martinelli and E. Scoppola, Commun. Math. Phys. 80 (1981), 223[CrossRef].
  15. G. Jona-Lasinio, F. Martinelli and E. Scoppola, Phys. Rep. 77 (1981), 313[CrossRef].
  16. B. Bleaney and J. H. Loubster, Nature 161 (1948), 522; Proc. Phys. Soc. London A 63 (1950), 483
  17. G. Birnbaum and A. Maryott, Phys. Rev. 92 (1953), 270[APS].
  18. G. Gallavotti, Riv. Nuovo Cim. 2 (1972), 133.
  19. R. E. Weston Jr., J. Am. Chem. Soc. 76 (1954), 2645[CrossRef].
  20. C. H. Townes and A. L. Schawlow, Microwave Spectroscopy (MacGraw-Hill, N.Y., 1955).
  21. S. Sachdev, Quantum Phase Transitions (Cambridge University Press, 1999).
  22. G. Jona-Lasinio and P. Claverie, Prog. Theor. Phys. Suppl. No. 86 (1986), 54[PTP].
  23. G. Jona-Lasinio and C. Presilla, in preparation.
  24. A. S. Wightman, in Probabistic Methods in Mathematical Physics, ed. F. Guerra, M. I. Loffredo and C. Marchioro (World Scientific, Singapore, 1992), p. 411; Nuovo Cim. B 110 (1995), 751.
  25. Y. Hosotani, Phys. Rev. D 51 (1995), 2022[APS].
  26. Kun Yang, Solid State Commun. 143 (2007), 27[CrossRef].
  27. A. H. Castro Nero et al., Rev. Mod. Phys. 81 (2009), 109[APS].
  28. L. Pasteur, Oeuvres complètes, Tome I (1922), 369.
  29. D. G. Blackmond, Cold Spring Harb. Perspect. Biol. 2 (2010), a002147.
  30. A. Salam, J. Mol. Evol. 33 (1991), 105.
  31. R. Plasson, H. Bersini and A. Commeyras, PNAS 101 (2004), 16733.
  32. M. Yoshimura, J. Phys. Soc. Jpn. 76 (2007), 111018[JPSJ].
  33. M. Shaposhnikov, J. Phys.: Conf. Ser. 171 (2009), 012005[IoP STACKS].
  34. L. Bertini, A. De Sole, D. Gabrielli, G. Jona-Lasinio and C. Landim, arXiv:1005.1489[e-print arXiv].
  35. L. Bertini, A. De Sole, D. Gabrielli, G. Jona-Lasinio and C. Landim, Phys. Rev. Lett. 94 (2005), 030601[APS]; J. Stat. Phys. 123 (2006), 237.
  36. T. Bodineau and B. Derrida, Phys. Rev. E 72 (2005), 066110[APS].

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