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Calculating Observables of Quantum Fields

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

Abstract

In this chapter, the task of computing hadron properties is outlined. We write path-integral representations of the relevant quantum-mechanical expectation value and then describe the best current method to compute this in a Monte Carlo calculation. Many of the mathematical tools and ideas introduced earlier will be important in writing efficient algorithms for these computations.

Keywords

Wilson Loop Gauge Field Topological Charge Creation Operator Quark Propagator 
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.
    J.J. Dudek, R.G. Edwards, M.J. Peardon, D.G. Richards, C.E. Thomas, Phys. Rev. D 82, 034508 (2010). doi: 10.1103/PhysRevD.82.034508 ADSCrossRefGoogle Scholar
  2. 2.
    M. Lüscher, Commun. Math. Phys. 54, 283 (1977). doi: 10.1007/BF01614090 ADSCrossRefGoogle Scholar
  3. 3.
    M. Creutz, Phys. Rev. D 15, 1128 (1977). doi: 10.1103/PhysRevD.15.1128 ADSCrossRefGoogle Scholar
  4. 4.
    N. Irges, F. Knechtli, Nucl. Phys. B 775, 283 (2007). doi: 10.1016/j.nuclphysb.2007.01.023 ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    M. Lüscher, U. Wolff, Nucl. Phys. B 339, 222 (1990). doi: 10.1016/0550-3213(90)90540-T ADSCrossRefGoogle Scholar
  6. 6.
    B. Blossier, M. Della Morte, G. von Hippel, T. Mendes, R. Sommer, JHEP 04, 094 (2009). doi: 10.1088/1126-6708/2009/04/094
  7. 7.
    R. Sommer, PoS LATTICE2013, 015 (2014)Google Scholar
  8. 8.
    M. Lüscher, JHEP 08, 071 (2010). doi: 10.1007/JHEP08(2010071,  10.1007/JHEP03(2014)092. [Erratum: JHEP03, 092 (2014)]
  9. 9.
    M. Lüscher, P. Weisz, JHEP 02, 051 (2011). doi: 10.1007/JHEP02(2011)051 ADSCrossRefGoogle Scholar
  10. 10.
    R. Narayanan, H. Neuberger, JHEP 03, 064 (2006). doi: 10.1088/1126-6708/2006/03/064 ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    M. Lüscher, Commun. Math. Phys. 293, 899 (2010). doi: 10.1007/s00220-009-0953-7 ADSCrossRefGoogle Scholar
  12. 12.
    R. Lohmayer, H. Neuberger, PoS LATTICE2011, 249 (2011)Google Scholar
  13. 13.
    S. Borsanyi et al., JHEP 09, 010 (2012). doi: 10.1007/JHEP09(2012)010 ADSCrossRefGoogle Scholar
  14. 14.
    A. Ramos, in Proceedings, 32nd International Symposium on Lattice Field Theory (Lattice 2014) (2015), https://inspirehep.net/record/1373921/files/arXiv:1506.00118.pdf
  15. 15.
    P. Fritzsch, A. Ramos, JHEP 10, 008 (2013). doi: 10.1007/JHEP10(2013)008 ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    M. Luscher, Commun. Math. Phys. 105, 153 (1986). doi: 10.1007/BF01211097 ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    K. Rummukainen, S.A. Gottlieb, Nucl. Phys. B 450, 397 (1995). doi: 10.1016/0550-3213(95)00313-H ADSCrossRefGoogle Scholar
  18. 18.
    C.B. Lang, D. Mohler, S. Prelovsek, M. Vidmar, Phys. Rev. D 84(5), 054503 (2011). doi: 10.1103/PhysRevD.89.059903,  10.1103/PhysRevD.84.054503. [Erratum: Phys. Rev. D89, no. 5, 059903 (2014)]
  19. 19.
    D.J. Wilson, R.A. Briceno, J.J. Dudek, R.G. Edwards, C.E. Thomas, Phys. Rev. D 92(9), 094502 (2015). doi: 10.1103/PhysRevD.92.094502 ADSCrossRefGoogle Scholar
  20. 20.
    M.T. Hansen, S.R. Sharpe, Phys. Rev. D 90(11), 116003 (2014). doi: 10.1103/PhysRevD.90.116003 ADSCrossRefGoogle Scholar
  21. 21.
    M. Albanese et al., Phys. Lett. B 192, 163 (1987). doi: 10.1016/0370-2693(87)91160-9 ADSCrossRefGoogle Scholar
  22. 22.
    M. Della Morte, A. Shindler, R. Sommer, JHEP 0508, 051 (2005)Google Scholar
  23. 23.
    C.W. Bernard, T.A. DeGrand, Nucl. Phys. Proc. Suppl. 83, 845 (2000). doi: 10.1016/S0920-5632(00)91822-X ADSCrossRefGoogle Scholar
  24. 24.
    A. Hasenfratz, F. Knechtli, Phys. Rev. D 64, 034504 (2001). doi: 10.1103/PhysRevD.64.034504 ADSCrossRefGoogle Scholar
  25. 25.
    A. Hasenfratz, R. Hoffmann, F. Knechtli, Nucl. Phys. Proc. Suppl. 106, 418 (2002). doi: 10.1016/S0920-5632(01)01733-9 [418 (2001)]
  26. 26.
    A. Grimbach, D. Guazzini, F. Knechtli, F. Palombi, JHEP 03, 039 (2008). doi: 10.1088/1126-6708/2008/03/039 Google Scholar
  27. 27.
    C. Morningstar, M.J. Peardon, Phys. Rev. D 69, 054501 (2004). doi: 10.1103/PhysRevD.69.054501 ADSCrossRefGoogle Scholar
  28. 28.
    S. Capitani, S. Durr, C. Hoelbling, JHEP 11, 028 (2006). doi: 10.1088/1126-6708/2006/11/028 ADSCrossRefGoogle Scholar
  29. 29.
    B. Berg, A. Billoire, Nucl. Phys. B 221, 109 (1983). doi: 10.1016/0550-3213(83)90620-X ADSCrossRefGoogle Scholar
  30. 30.
    G.S. Bali, K. Schilling, A. Hulsebos, A.C. Irving, C. Michael, P.W. Stephenson, Phys. Lett. B 309, 378 (1993). doi: 10.1016/0370-2693(93)90948-H ADSCrossRefGoogle Scholar
  31. 31.
    C.J. Morningstar, M.J. Peardon, Phys. Rev. D 60, 034509 (1999). doi: 10.1103/PhysRevD.60.034509 ADSCrossRefGoogle Scholar
  32. 32.
    M. Donnellan, F. Knechtli, B. Leder, R. Sommer, Nucl. Phys. B 849, 45 (2011). doi: 10.1016/j.nuclphysb.2011.03.013 ADSCrossRefGoogle Scholar
  33. 33.
    R. Sommer, (2010)Google Scholar
  34. 34.
    G. Parisi, R. Petronzio, F. Rapuano, Phys. Lett. B 128, 418 (1983). doi: 10.1016/0370-2693(83)90930-9 ADSCrossRefGoogle Scholar
  35. 35.
    G.S. Bali, K. Schilling, C. Schlichter, Phys. Rev. D 51, 5165 (1995). doi: 10.1103/PhysRevD.51.5165 ADSCrossRefGoogle Scholar
  36. 36.
    M. Lüscher, P. Weisz, JHEP 09, 010 (2001). doi: 10.1088/1126-6708/2001/09/010 CrossRefGoogle Scholar
  37. 37.
    S. Necco, R. Sommer, Nucl. Phys. B 622, 328 (2002). doi: 10.1016/S0550-3213(01)00582-X ADSCrossRefGoogle Scholar
  38. 38.
    M. Della Morte, S. Durr, J. Heitger, H. Molke, J. Rolf, A. Shindler, R. Sommer, Phys. Lett. B581, 93 (2004). doi: 10.1016/j.physletb.2005.03.017
  39. 39.
    P. Weisz, Nucl. Phys. B 212, 1 (1983). doi: 10.1016/0550-3213(83)90595-3 ADSMathSciNetCrossRefGoogle Scholar
  40. 40.
    M. Lüscher, K. Symanzik, P. Weisz, Nucl. Phys. B 173, 365 (1980). doi: 10.1016/0550-3213(80)90009-7 ADSCrossRefGoogle Scholar
  41. 41.
    M. Lüscher, Nucl. Phys. B 180, 317 (1981). doi: 10.1016/0550-3213(81)90423-5 ADSCrossRefGoogle Scholar
  42. 42.
    Y. Nambu, Phys. Lett. B 80, 372 (1979). doi: 10.1016/0370-2693(79)91193-6 ADSCrossRefGoogle Scholar
  43. 43.
    M. Lüscher, P. Weisz, JHEP 07, 049 (2002). doi: 10.1088/1126-6708/2002/07/049 CrossRefGoogle Scholar
  44. 44.
    M. Lüscher, G. Münster, P. Weisz, Nucl. Phys. B 180, 1 (1981). doi: 10.1016/0550-3213(81)90151-6 ADSCrossRefGoogle Scholar
  45. 45.
    F. Gliozzi, M. Pepe, U.J. Wiese, Phys. Rev. Lett. 104, 232001 (2010). doi: 10.1103/PhysRevLett.104.232001 ADSCrossRefGoogle Scholar
  46. 46.
    R. Sommer, Nucl. Phys. B 411, 839 (1994). doi: 10.1016/0550-3213(94)90473-1 ADSCrossRefGoogle Scholar
  47. 47.
    M. Guagnelli, R. Sommer, H. Wittig, Nucl. Phys. B 535, 389 (1998). doi: 10.1016/S0550-3213(98)00599-9 ADSCrossRefGoogle Scholar
  48. 48.
    C.W. Bernard, T. Burch, K. Orginos, D. Toussaint, T.A. DeGrand, C.E. DeTar, S.A. Gottlieb, U.M. Heller, J.E. Hetrick, B. Sugar, Phys. Rev. D 62, 034503 (2000). doi: 10.1103/PhysRevD.62.034503 ADSCrossRefGoogle Scholar
  49. 49.
    B. Leder, F. Knechtli, PoS LATTICE2011, 315 (2011)Google Scholar
  50. 50.
    M. Lüscher, R. Narayanan, P. Weisz, U. Wolff, Nucl. Phys. B 384, 168 (1992). doi: 10.1016/0550-3213(92)90466-O ADSCrossRefGoogle Scholar
  51. 51.
    M. Creutz, Acta Phys. Slov. 61, 1 (2011). doi: 10.2478/v10155-011-0001-y ADSCrossRefGoogle Scholar
  52. 52.
    E. Witten, Nucl. Phys. B 156, 269 (1979). doi: 10.1016/0550-3213(79)90031-2 ADSCrossRefGoogle Scholar
  53. 53.
    G. Veneziano, Nucl. Phys. B 159, 213 (1979). doi: 10.1016/0550-3213(79)90332-8 ADSMathSciNetCrossRefGoogle Scholar
  54. 54.
    C. Gattringer, C.B. Lang, Lect. Notes Phys. 788, 1 (2010). doi: 10.1007/978-3-642-01850-3 ADSMathSciNetCrossRefGoogle Scholar
  55. 55.
    M. Bruno, S. Schaefer, R. Sommer, JHEP 08, 150 (2014). doi: 10.1007/JHEP08(2014)150 ADSCrossRefGoogle Scholar
  56. 56.
    M.F. Atiyah, I.M. Singer, Annals Math. 93, 139 (1971). doi: 10.2307/1970757 MathSciNetCrossRefGoogle Scholar
  57. 57.
    P. Hasenfratz, V. Laliena, F. Niedermayer, Phys. Lett. B 427, 125 (1998). doi: 10.1016/S0370-2693(98)00315-3 ADSCrossRefGoogle Scholar
  58. 58.
    M. Peardon, J. Bulava, J. Foley, C. Morningstar, J. Dudek, R.G. Edwards, B. Joo, H.W. Lin, D.G. Richards, K.J. Juge, Phys. Rev. D 80, 054506 (2009). doi: 10.1103/PhysRevD.80.054506 ADSCrossRefGoogle Scholar
  59. 59.
    C. Morningstar, J. Bulava, J. Foley, K.J. Juge, D. Lenkner, M. Peardon, C.H. Wong, Phys. Rev. D 83, 114505 (2011). doi: 10.1103/PhysRevD.83.114505 ADSCrossRefGoogle Scholar
  60. 60.
    S. Capstick, N. Isgur, Phys. Rev. D 34, 2809 (1986). doi: 10.1103/PhysRevD.34.2809,  10.1063/1.35361 [AIP Conf. Proc. 132, 267 (1985)]
  61. 61.
    S. Basak, R.G. Edwards, G.T. Fleming, U.M. Heller, C. Morningstar, D. Richards, I. Sato, S. Wallace, Phys. Rev. D 72, 094506 (2005). doi: 10.1103/PhysRevD.72.094506 ADSCrossRefGoogle Scholar
  62. 62.
    R.G. Edwards, J.J. Dudek, D.G. Richards, S.J. Wallace, Phys. Rev. D 84, 074508 (2011). doi: 10.1103/PhysRevD.84.074508 ADSCrossRefGoogle Scholar
  63. 63.
    G.P. Lepage, in Boulder ASI 1989: 97–120, pp. 97–120 (1989), http://alice.cern.ch/format/showfull?sysnb=0117836
  64. 64.
    G.S. Bali, H. Neff, T. Duessel, T. Lippert, K. Schilling, Phys. Rev. D 71, 114513 (2005). doi: 10.1103/PhysRevD.71.114513 ADSCrossRefGoogle Scholar
  65. 65.
    F. Knechtli, R. Sommer, Phys. Lett. B 440(345), 1998 (1999). doi: 10.1016/S0370-2693(98)01098-3 Erratum-ibid. B454: 399
  66. 66.
    F. Knechtli, R. Sommer, Nucl. Phys. B 590, 309 (2000). doi: 10.1016/S0550-3213(00)00470-3 ADSCrossRefGoogle Scholar
  67. 67.
    O. Philipsen, H. Wittig, Phys. Rev. Lett. 81, 4056 (1998). doi: 10.1103/PhysRevLett.81.4056 [Erratum: Phys. Rev. Lett. 83, 2684 (1999)]
  68. 68.
    V. Koch, J. Bulava, B. Hrz, F. Knechtli, G. Moir, C. Morningstar, M. Peardon, (2015)Google Scholar
  69. 69.
    U. Wolff, Comput. Phys. Commun. 156, 143 (2004). doi: 10.1016/S0010-4655(03)00467-3,  10.1016/j.cpc.2006.12.001 [Erratum: Comput. Phys. Commun. 176, 383 (2007)]
  70. 70.
    W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes 3rd Edition: The Art of Scientific Computing, 3rd edn. (Cambridge University Press, New York, NY, USA, 2007)zbMATHGoogle 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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