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Quantum Field Theory (QFT) on the Lattice

  • Francesco KnechtliEmail author
  • Michael Günther
  • Michael Peardon
Chapter
  • 885 Downloads
Part of the SpringerBriefs in Physics book series (SpringerBriefs in Physics)

Abstract

In 1964, Gell-Mann [1] and Zweig [2] proposed that hadrons, the particles which experience strong interactions, are made of quarks. Quarks are confined within hadrons and never seen in isolation. Electron-nucleon scattering experiments at large momentum transfer could be explained by assuming the nucleon is made of almost-free point-like constituents called partons [3, 4, 5].

Keywords

Partition Function Gauge Transformation Wilson Loop Dirac Operator Chiral Symmetry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    M. Gell-Mann, Phys. Lett. 8, 214 (1964)ADSCrossRefGoogle Scholar
  2. 2.
    G. Zweig, Preprints CERN-TH 401 and 412 (1964)Google Scholar
  3. 3.
    J.D. Bjorken, E.A. Paschos, Phys. Rev. 185, 1975 (1969)ADSCrossRefGoogle Scholar
  4. 4.
    R.P. Feynman, Gordon and Breach, p. 237 (1970)Google Scholar
  5. 5.
    R.P. Feynman, Phys. Rev. Lett. 23, 1415 (1969)ADSCrossRefGoogle Scholar
  6. 6.
    H. Fritzsch, M. Gell-Mann, H. Leutwyler, Phys. Lett. 47B, 365 (1973)ADSCrossRefGoogle Scholar
  7. 7.
    H. Weyl, Z. Phys. 56, 330 (1929)ADSCrossRefGoogle Scholar
  8. 8.
    G.’t Hooft, unpublished. See, however, Proceedings of Colloquium on Renormalization of Yang-Mills Fields and Applications to Particle Physics, Marseilles, 1972, ed. by C.P. Korthals-Altes. See also Nucl. Phys. B254, 11 (1985)Google Scholar
  9. 9.
    D.J. Gross, F. Wilczek, Phys. Rev. Lett. 30, 1343 (1973)ADSCrossRefGoogle Scholar
  10. 10.
    H.D. Politzer, Phys. Rev. Lett. 30, 1346 (1973)ADSCrossRefGoogle Scholar
  11. 11.
    P. Söding, Eur. Phys. J. H35, 3 (2010). doi: 10.1140/epjh/e2010-00002-5 ADSGoogle Scholar
  12. 12.
    K.G. Wilson, Phys. Rev. D 10, 2445 (1974). doi: 10.1103/PhysRevD.10.2445 ADSCrossRefGoogle Scholar
  13. 13.
    K.G. Wilson, Nucl. Phys. Proc. Suppl. 140, 3 (2005). doi: 10.1016/j.nuclphysbps.2004.11.271.[,3(2004)] ADSCrossRefGoogle Scholar
  14. 14.
    I. Montvay, G. Münster, Quantum Fields on a Lattice (Univ. Pr., Cambridge, UK, 1994), p. 491 (Cambridge monographs on mathematical physics), http://www.slac.stanford.edu/spires/find/hep/www?key=3030474
  15. 15.
    T. DeGrand, C. DeTar, Lattice Methods for Quantum Chromodynamics (World Scientific, Singapure, 2006)Google Scholar
  16. 16.
    U. Wolff, Quantum Field Theory, lecture note, HU Berlin, unpublished (2010)Google Scholar
  17. 17.
    J. Smit, Cambridge. Lect. Notes Phys. 15, 1 (2002)Google Scholar
  18. 18.
    M. Creutz, in Quarks, Gluons and Lattices. Cambridge Monographs on Mathematical Physics (Cambridge Univ. Press, Cambridge, UK, 1985), http://www-spires.fnal.gov/spires/find/books/www?cl=QC793.3.F5C73::1983
  19. 19.
    M. Bochicchio, L. Maiani, G. Martinelli, G.C. Rossi, M. Testa, Nucl. Phys. B 262, 331 (1985). doi: 10.1016/0550-3213(85)90290-1 ADSCrossRefGoogle Scholar
  20. 20.
    M. Lüscher, S. Sint, R. Sommer, P. Weisz, Nucl. Phys. B 478, 365 (1996). doi: 10.1016/0550-3213(96)00378-1 ADSCrossRefGoogle Scholar
  21. 21.
    H.B. Nielsen, M. Ninomiya, Phys. Lett. B 105, 219 (1981). doi: 10.1016/0370-2693(81)91026-1 ADSCrossRefGoogle Scholar
  22. 22.
    H.B. Nielsen, M. Ninomiya, Nucl. Phys. B 185(20), 1981 (1982). doi: 10.1016/0550-3213(81)90361-8.[Erratum:Nucl.Phys.B195541] MathSciNetGoogle Scholar
  23. 23.
    H.B. Nielsen, M. Ninomiya, Nucl. Phys. B 193, 173 (1981). doi: 10.1016/0550-3213(81)90524-1 ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    D. Friedan, Commun. Math. Phys. 85, 481 (1982). doi: 10.1007/BF01403500 ADSMathSciNetCrossRefGoogle Scholar
  25. 25.
    M. Lüscher, Phys. Lett. B 428, 342 (1998). doi: 10.1016/S0370-2693(98)00423-7 ADSCrossRefGoogle Scholar
  26. 26.
    M. Lüscher, Commun. Math. Phys. 54, 283 (1977). doi: 10.1007/BF01614090 ADSCrossRefGoogle Scholar
  27. 27.
    J.B. Kogut, L. Susskind, Phys. Rev. D 11, 395 (1975). doi: 10.1103/PhysRevD.11.395 ADSCrossRefGoogle Scholar
  28. 28.
    L. Susskind, Phys. Rev. D 16, 3031 (1977). doi: 10.1103/PhysRevD.16.3031 ADSCrossRefGoogle Scholar
  29. 29.
    H.S. Sharatchandra, H.J. Thun, P. Weisz, Nucl. Phys. B 192, 205 (1981). doi: 10.1016/0550-3213(81)90200-5 ADSCrossRefGoogle Scholar
  30. 30.
    B. Bunk, M. Della Morte, K. Jansen, F. Knechtli. Nucl. Phys. B697, 343 (2004). doi: 10.1016/j.nuclphysb.2004.07.023
  31. 31.
    P.H. Ginsparg, K.G. Wilson, Phys. Rev. D 25, 2649 (1982). doi: 10.1103/PhysRevD.25.2649 ADSCrossRefGoogle Scholar
  32. 32.
    P. Hasenfratz, V. Laliena, F. Niedermayer, Phys. Lett. B 427, 125 (1998). doi: 10.1016/S0370-2693(98)00315-3 ADSCrossRefGoogle Scholar
  33. 33.
    H. Neuberger, Phys. Lett. B 417, 141 (1998). doi: 10.1016/S0370-2693(97)01368-3 ADSMathSciNetCrossRefGoogle Scholar
  34. 34.
    P. Hernandez, K. Jansen, M. Luscher, Nucl. Phys. B 552, 363 (1999). doi: 10.1016/S0550-3213(99)00213-8 ADSMathSciNetCrossRefGoogle Scholar
  35. 35.
    J. Brannick, A. Frommer, K. Kahl, B. Leder, M. Rottmann, A. Strebel, Numer. Math. (2015). doi: 10.1007/s00211-015-0725-6 Google Scholar
  36. 36.
    W. Bietenholz, U. Gerber, M. Pepe, U.J. Wiese, JHEP 12, 020 (2010). doi: 10.1007/JHEP12(2010)020 ADSCrossRefGoogle Scholar
  37. 37.
    P. Weisz, in Modern Perspectives in Lattice QCD: Quantum Field Theory and High Performance Computing. Proceedings, International School, 93rd Session, Les Houches, France, August 3–28, 2009 (2010), pp. 93–160, https://inspirehep.net/record/852286/files/arXiv:1004.3462.pdf
  38. 38.
    M. Lüscher, P. Weisz, Commun. Math. Phys. 97, 59 (1985). doi: 10.1007/BF01206178 ADSCrossRefGoogle Scholar
  39. 39.
    M. Lüscher, in Probing the Standard Model of Particle Interactions. Proceedings, Summer School in Theoretical Physics, NATO Advanced Study Institute, 68th Session, Les Houches, France, July 28-September 5, 1997. Pt. 1, 2 (1998), pp. 229–280, http://alice.cern.ch/format/showfull?sysnb=0270921
  40. 40.
    J. Zinn-Justin, Lect. Notes Phys. 659, 167 (2005)ADSMathSciNetGoogle Scholar
  41. 41.
    K. Symanzik, in Recent Developments in Gauge Theories (Cargèse 1979), ed. by G. ’t Hooft et al. (Plenum, New York, 1980)Google Scholar
  42. 42.
    P. Weisz, Nucl. Phys. B 212, 1 (1983). doi: 10.1016/0550-3213(83)90595-3 ADSMathSciNetCrossRefGoogle Scholar
  43. 43.
    K. Symanzik, in Mathematical Problems in Theoretical Physics, ed. by R. Schrader et al. Lecture Notes in Physics, vol. 153 (Springer, New York, 1982)Google Scholar
  44. 44.
    K. Symanzik, Nucl. Phys. B 226, 187 (1983). doi: 10.1016/0550-3213(83)90468-6 ADSMathSciNetCrossRefGoogle Scholar
  45. 45.
    K. Symanzik, Nucl. Phys. B 226, 205 (1983). doi: 10.1016/0550-3213(83)90469-8 ADSMathSciNetCrossRefGoogle Scholar
  46. 46.
    K. Wilson, in Recent Developments in Gauge Theories (Cargèse 1979), ed. by G. ’t Hooft et al. (Plenum, New York, 1980)Google Scholar
  47. 47.
    M. Lüscher, P. Weisz, Phys. Lett. B 158, 250 (1985). doi: 10.1016/0370-2693(85)90966-9 ADSCrossRefGoogle Scholar
  48. 48.
    B. Sheikholeslami, R. Wohlert, Nucl. Phys. B 259, 572 (1985). doi: 10.1016/0550-3213(85)90002-1 ADSCrossRefGoogle Scholar
  49. 49.
    G. Heatlie, G. Martinelli, C. Pittori, G.C. Rossi, C.T. Sachrajda, Nucl. Phys. B 352, 266 (1991). doi: 10.1016/0550-3213(91)90137-M ADSCrossRefGoogle Scholar
  50. 50.
    R. Frezzotti, P.A. Grassi, S. Sint, P. Weisz, JHEP 0108, 058 (2001)Google Scholar
  51. 51.
    S. Sint, in Workshop on Perspectives in Lattice QCD Nara, Japan, October 31–November 11, 2005 (2007)Google Scholar
  52. 52.
    R. Frezzotti, G.C. Rossi, JHEP 08, 007 (2004). doi: 10.1088/1126-6708/2004/08/007 ADSCrossRefGoogle Scholar
  53. 53.
    S. Capitani, Phys. Rep. 382, 113 (2003). doi: 10.1016/S0370-1573(03)00211-4 ADSMathSciNetCrossRefGoogle Scholar
  54. 54.
    H.J. Rothe, World Sci. Lect. Notes Phys. 43, 1 (1992). [World Sci. Lect. Notes Phys.82,1(2012)]Google Scholar
  55. 55.
    C. Gattringer, C.B. Lang, Lect. Notes Phys. 788, 1 (2010). doi: 10.1007/978-3-642-01850-3 ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© The Author(s) 2017

Authors and Affiliations

  • Francesco Knechtli
    • 1
    Email author
  • Michael Günther
    • 2
  • Michael Peardon
    • 3
  1. 1.Department of Physics, School of Mathematics and Natural SciencesUniversity of WuppertalWuppertalGermany
  2. 2.Department of Mathematics, School of Mathematics and Natural SciencesUniversity of WuppertalWuppertalGermany
  3. 3.School of MathematicsTrinity College DublinDublin 2Ireland

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