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Basics of QCD and Lattice QCD

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Lattice QCD Study for the Relation Between Confinement and Chiral Symmetry Breaking

Part of the book series: Springer Theses ((Springer Theses))

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Abstract

In this chapter, we review the basics and motivations of this thesis. The main subject of this paper is the relation between the non-perturbative phenomena such as quark-confinement and chiral symmetry breaking in QCD. First of all, I review the basics of QCD, including order parameters for confinement and Banks–Casher relation. In particular, the Banks–Casher relation shows the relation between chiral symmetry breaking and Dirac eigenmodes, and it is important formula in this thesis. Then, we review the lattice QCD, which is essential formalism for non-perturbative analysis of QCD. Finally, the motivation and outline of this thesis are shown.

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Notes

  1. 1.

    In the cases of finite temperature with zero chemical potential, color SU(2), imaginary chemical potential, or isospin chemical potential, the Monte-Carlo simulation can be performed.

References

  1. M.E. Peskin, D.V. Schroeder, An Introduction to Quantum Field Theory, (Perseus Books, 1995)

    Google Scholar 

  2. C.N. Yang, R.L. Mill, Phys. Rev. 96, 191 (1954)

    Article  ADS  Google Scholar 

  3. D.J. Gross, F. Wilczek, Phys. Rev. Lett. 30, 1343 (1973)

    Article  ADS  Google Scholar 

  4. H.D. Politzer, Phys. Rev. Lett. 30, 1346 (1973)

    Article  ADS  Google Scholar 

  5. J. Greensite, An Introduction to the Confinement Problem, (Springer, Berlin, 2011)

    Google Scholar 

  6. E. Eichten, K. Gottfried, T. Kinoshita, J. Kogut, K.D. Lane, T.M. Yan, Phys. Rev. Lett. 34, 369 (1975); Phys. Rev. Lett. 36, 1276 (1976)

    Google Scholar 

  7. G.S. Bali, K. Schilling, C. Schlichter, Phys. Rev. D 51, 5165 (1995)

    Article  ADS  Google Scholar 

  8. G.S. Bali, Phys. Rept. 343, 1 (2001)

    Article  ADS  Google Scholar 

  9. H. Ichie, V. Bornyakov, T. Streuer, G. Schierholz, Nucl. Phys. A 721, 899 (2003)

    Article  ADS  Google Scholar 

  10. T.T. Takahashi, H. Suganuma, H. Ichie, H. Matsufuru, Y. Nemoto, Nucl. Phys. A 721, 926 (2003)

    Article  ADS  Google Scholar 

  11. V.G. Bornyakov et al., DIK collaboration. Phys. Rev. D 70, 054506 (2004)

    Article  ADS  Google Scholar 

  12. H.J. Rothe, Lattice Gauge Theories, (World Scientific, 2012)

    Google Scholar 

  13. L.D. McLerran, B. Svetitsky, Phys. Rev. D 24, 450 (1981)

    Article  ADS  Google Scholar 

  14. Y. Nambu, Phys. Rev. D 10, 4262 (1974)

    Article  ADS  Google Scholar 

  15. G. ’t Hooft, in Proceedings of High Energy Physics, (Editrice Compositori, 1976)

    Google Scholar 

  16. S. Mandelstam, Phys. Rep. C 23, 245 (1976)

    Article  ADS  Google Scholar 

  17. G. ’t Hooft, Nucl. Phys. B190, 455 (1981)

    Google Scholar 

  18. H. Suganuma, S. Sasaki, H. Toki, Nucl. Phys. B 435, 207 (1995)

    Article  ADS  Google Scholar 

  19. O. Miyamura, Phys. Lett. B 353, 91 (1995)

    Article  ADS  Google Scholar 

  20. R.M. Woloshyn, Phys. Rev. D 51, 6411 (1995)

    Article  ADS  Google Scholar 

  21. N. Sakumichi, H. Suganuma, Phys. Rev. D 90, 111501 (2014)

    Article  ADS  Google Scholar 

  22. Y.M. Cho, F.H. Cho, J.H. Yoon, Phys. Rev. D 87, 085025 (2013)

    Article  ADS  Google Scholar 

  23. L. Faddeev, A. Niemi, Phys. Rev. Lett. 82, 1624 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  24. S. Kato, K. Kondo, T. Murakami, A. Shibata, T. Shinohara, S. Ito, Phys. Lett. B 632, 326 (2006)

    Article  ADS  Google Scholar 

  25. T. Kugo, I. Ojima, Prog. Theor. Phys. Suppl. 66, 1 (1979)

    Article  ADS  Google Scholar 

  26. S. Furui, H. Nakajima, Phys. Rev. D 69, 074505 (2004)

    Article  ADS  Google Scholar 

  27. N. Yamanaka, T.M. Doi, S. Imai, H. Suganuma, Phys. Rev. D 88, 074036 (2013)

    Article  ADS  Google Scholar 

  28. N. Yamanaka, S. Imai, T.M. Doi, H. Suganuma, Phys. Rev. D 89, 074017 (2014)

    Article  ADS  Google Scholar 

  29. Y. Nambu and G. Jona-Lasinio, Phys. Rev. 122, 345 (1961); 124, 246 (1961)

    Google Scholar 

  30. J. Goldstone, Nuovo Cim. 19, 154 (1961)

    Article  ADS  MathSciNet  Google Scholar 

  31. J. Goldstone, A. Salam, S. Weinberg, Phys. Rev. 127, 965 (1962)

    Article  ADS  MathSciNet  Google Scholar 

  32. T. Banks, A. Casher, Nucl. Phys. B 169, 103 (1980)

    Article  ADS  Google Scholar 

  33. K.G. Wilson, Phys. Rev. D 10, 2445 (1974)

    Article  ADS  Google Scholar 

  34. M. Creutz, Quarks (Cambridge University Press, Gluons and Lattices, 1983)

    Google Scholar 

  35. H.B. Nielsen, M. Ninomiya, Nucl. Phys. B 185, 20 (1981)

    Article  ADS  Google Scholar 

  36. H.B. Nielsen, M. Ninomiya, Nucl. Phys. B 193, 173 (1981)

    Article  ADS  Google Scholar 

  37. M.G. Alford, K. Rajagopal, F. Wilczek, Phys. Lett. B 422, 247 (1998)

    Article  ADS  Google Scholar 

  38. M.G. Alford, K. Rajagopal, F. Wilczek, Nucl. Phys. B 537, 443 (1999)

    Article  ADS  Google Scholar 

  39. R. Rapp, T. Schaefer, E.V. Shuryak, M. Velkovsky, Phys. Rev. Lett. 81, 53 (1998)

    Article  ADS  Google Scholar 

  40. K. Fukushima, C. Sasaki, Prog. Part. Nucl. Phys. 72, 99 (2013)

    Article  ADS  Google Scholar 

  41. K. Fukushima, T. Hatsuda, Rept. Prog. Phys. 74, 014001 (2011)

    Article  ADS  Google Scholar 

  42. Z. Fodor, S.D. Katz, Phys. Lett. B 534, 87 (2002)

    Article  ADS  Google Scholar 

  43. D.T. Son, A. Misha, Stephanov. Phys. Rev. Lett. 86, 592 (2001)

    Article  ADS  Google Scholar 

  44. P. de Forcrand, O. Philipsen, Nucl. Phys. B 642, 290 (2002)

    Article  ADS  Google Scholar 

  45. S. Muroya, A. Nakamura, C. Nonaka, T. Takaishi, Prog. Theor. Phys. 110, 615 (2003)

    Article  ADS  Google Scholar 

  46. C. Gattringer, Phys. Rev. Lett. 97, 032003 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  47. F. Bruckmann, C. Gattringer, C. Hagen, Phys. Lett. B 647, 56 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  48. E. Bilgici, F. Bruckmann, C. Gattringer, C. Hagen, Phys. Rev. D 77, 094007 (2008)

    Article  ADS  Google Scholar 

  49. Y. Hatta, K. Fukushima, Phys. Rev. D 69, 097502 (2004)

    Article  ADS  Google Scholar 

  50. C.B. Lang, M. Schrock, Phys. Rev. D 84, 087704 (2011); L.Ya. Glozman, C.B. Lang, and M. Schrock. Phys. Rev. D 86, 014507 (2012)

    Google Scholar 

  51. S. Gongyo, T. Iritani, H. Suganuma, Phys. Rev. D 86, 034510 (2012)

    Article  ADS  Google Scholar 

  52. T. Iritani, H. Suganuma, PTEP 2014, 033B03 (2014)

    Google Scholar 

  53. F. Synatschke, A. Wipf, K. Langfeld, Phys. Rev. D 77, 114018 (2008)

    Article  ADS  Google Scholar 

  54. J. Kogut, M. Stone, H.W. Wyld, W.R. Gibbs, J. Shigemitsu, S.H. Shenker, D.K. Sinclair, Phys. Rev. Lett. 50, 393 (1983)

    Article  ADS  Google Scholar 

  55. F. Karsch, Lect. Notes Phys. 583, 209 (2002)

    Article  ADS  Google Scholar 

  56. J.D. Stack, S.D. Neiman, R.J. Wensley, Phys. Rev. D 424(50), 3399 (1994)

    Article  ADS  Google Scholar 

  57. H. Suganuma, A. Tanaka, S. Sasaki, and O. Miyamura, Nucl. Phys. B47; Proc. Suppl., 302 (1996)

    Google Scholar 

  58. Y. Aoki, Z. Fodor, S.D. Katz, K.K. Szabo, Phys. Lett. B 643, 46 (2006)

    Article  ADS  Google Scholar 

  59. Y. Aoki, S. Borsanyl, S. Durr, Z. Fodor, S.D. Katz, S. Krieg, K.K. Szabo, JHEP 06, 088 (2009)

    Article  ADS  Google Scholar 

  60. T. Bhattacharya et al., Phys. Rev. Lett. 113, 082001 (2014)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Nishina Center, RIKEN, Saitama, Japan

    Takahiro Doi

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  1. Takahiro Doi
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Correspondence to Takahiro Doi .

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Doi, T. (2017). Basics of QCD and Lattice QCD. In: Lattice QCD Study for the Relation Between Confinement and Chiral Symmetry Breaking. Springer Theses. Springer, Singapore. https://doi.org/10.1007/978-981-10-6596-5_1

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