Quantum chromodynamics (QCD) is the fundamental quantum field theory of quarks and gluons. To discuss it in a mathematically well-defined way, the theory has to be regularized by replacing space-time with a Euclidean lattice. This regularized theory, called lattice QCD (LQCD), has proven to be an efficient approach which allows for both theoretical understanding and computational analysis. LQCD has become a standard tool in elementary particle physics, which can be solved by the hybrid Monte Carlo method. The calculation of force is most difficult part in the hybrid Monte Carlo method. This lecture gives the details of the force calculation in one-loop Symanzik improved action, Wilson fermion with clover term, asqtad fermion, HISQ fermion, rooted staggered fermion, smeared fermion, staggered Wilson fermion, overlap fermion and domain wall fermion. The even-odd precondition are also considered in these calculations.
| Published in | American Journal of Physics and Applications (Volume 10, Issue 1) |
| DOI | 10.11648/j.ajpa.20221001.12 |
| Page(s) | 8-23 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Lattice QCD, Wilson Gauge Action, Fermion Action, Force Calculation
| [1] | K. G. Wilson, Phys. Rev. D 10 (1974), 2445. |
| [2] | M. Creutz, Phys. Rev. D 21 (1980), 2308. |
| [3] | I. Montvay, G. Munster, Quantum Fields on a Lattice, Cambridge University Press, Cambridge, 1994. |
| [4] | R. Gupta, Introduction to Lattice QCD, hep-lat/9807028. |
| [5] | H. J. Rothe, World Sci. Lect. Notes Phys. 74, 1 (2005). |
| [6] | J. Smit, Cambridge Lect. Notes Phys. 15, 1 (2002). |
| [7] | C. Gattringer and C. Lang, Quantum Chromodynamics on the Lattice: An Introductory Presentation, Lecture Notes in Physics, Springer Berlin Heidelberg, 2009. |
| [8] | Y. Aoki, etc., arXiv:2111.09849. |
| [9] | M. Alford, W. Dimm, G. P. Lepage, G. Hockney, P. B. Mackenzie, Phys. Lett. B 361 (1995), 87. |
| [10] | B. Sheikholeslami and R. Wohlert, Nucl. Phys. B 259, 572 (1985) 216. |
| [11] | M. Lüscher and P. Weisz, Nucl. Phys. B 479, 429 (1996) 219. |
| [12] | G. P. Lepage and P. B. Mackenzie, Phys. Rev. D 48, 2250 (1993) 219. |
| [13] | T. DeGrand and C. DeTar, Lattice Methods for Quantum Chromodynamics (World Scientific, Singapore 2006) 219. |
| [14] | K. Jansen and R. Sommer, Nucl. Phys. B 530, 185 (1998) 221. |
| [15] | G. P. Lepage, Phys. Rev. D 59 (1999), 074502. |
| [16] | A. Bazavov, D. Toussaint, C. Bernard, etc., Rev. Mod. Phys. 82 (2010), 1349. |
| [17] | S. Naik, Nucl. Phys. B 316 (1989), 238. |
| [18] | E. Follana, Q. Mason, C. Davies, K. Hornbostel, G. P. Lepage, J. Shigemitsu, H. Trottier, and K. Wong, Phys. Rev. D 75 (2007), 054502. |
| [19] | C. T. H. Davies et al., Phys. Rev. D 82 (2010), 114504. |
| [20] | C. McNeile et al., Phys. Rev. D 85 (2012), 031503. |
| [21] | G. C. Donald et al., Phys. Rev. D 86 (2012), 094501. |
| [22] | T. DeGrand, A. Hasenfratz, T. Kovacs, Nucl. Phys. B 547 (1999), 258. |
| [23] | T. DeGrand, S. Schaefer, Phys. Rev. D 71 (2005), 034507. |
| [24] | T. DeGrand, S. Schaefer, Phys. Rev. D 72 (2005), 054503. |
| [25] | A. Hasenfratz, F. Knectli, Phys. Rev. D 64 (2005), 034504. |
| [26] | A. Hasenfratz, R. Hoffmann, S. Schaefer, J. High Energy Phys. (2007), 029. |
| [27] | D. H. Adams, Phys. Rev. Lett. 104 (2010) 141602. |
| [28] | D. H. Adams, Phys. Lett. B 699 (2011) 394. |
| [29] | H. Neuberger, Phys. Lett. B 427, 353 (1998) 164. |
| [30] | A. Borici, NATO Sci. Ser. C 553, 41 (2000), [hep- lat/9912040]. |
| [31] | A. D. Kennedy (2006), [hep-lat/0607038]. |
| [32] | D. B. Kaplan, Phys. Lett. B 288 (1992) 342. |
| [33] | Y. Shamir, Nucl. Phys. B 406 (1993) 90. |
| [34] | Y. Shamir: Phys. Rev. Lett. 71 (1993) 2691. |
| [35] | V. Furman and Y. Shamir: Nucl. Phys. B 439 (1995) 54. |
| [36] | P. Hasenfratz, hep-lat/9803027. |
| [37] | W. Bietenholz, R. Brower, S. Chandrasekharan, and U.-J. Wiese, Nucl. Phys. (Proc. Suppl.) B 53 (1997) 921. |
| [38] | M. Alford, T. Klassen, and P. Lepage, Phys. Rev. D 58 (1998), 034503. |
| [39] | P. Lepage and B. Thacker, Phys. Rev. D 43 (1991) 196; G. Lepage, L. Magnea, C. Nakhleh, U. Magnea and K. Hornbostel, Phys. Rev. D 46 (1992) 4052. |
| [40] | A. Ali Khan, et al., Phys. Lett. B 427 (1998) 132. |
| [41] | A. X. El-Khadra, A. S. Kronfeld, P. B. Mackenzie, Phys. Rev. D 55 (1997) 3933. |
APA Style
Daming Li. (2022). The Calculation of Force in Lattice Quantum Chromodynamics. American Journal of Physics and Applications, 10(1), 8-23. https://doi.org/10.11648/j.ajpa.20221001.12
ACS Style
Daming Li. The Calculation of Force in Lattice Quantum Chromodynamics. Am. J. Phys. Appl. 2022, 10(1), 8-23. doi: 10.11648/j.ajpa.20221001.12
AMA Style
Daming Li. The Calculation of Force in Lattice Quantum Chromodynamics. Am J Phys Appl. 2022;10(1):8-23. doi: 10.11648/j.ajpa.20221001.12
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.ajpa.20221001.12,
author = {Daming Li},
title = {The Calculation of Force in Lattice Quantum Chromodynamics},
journal = {American Journal of Physics and Applications},
volume = {10},
number = {1},
pages = {8-23},
doi = {10.11648/j.ajpa.20221001.12},
url = {https://doi.org/10.11648/j.ajpa.20221001.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajpa.20221001.12},
abstract = {Quantum chromodynamics (QCD) is the fundamental quantum field theory of quarks and gluons. To discuss it in a mathematically well-defined way, the theory has to be regularized by replacing space-time with a Euclidean lattice. This regularized theory, called lattice QCD (LQCD), has proven to be an efficient approach which allows for both theoretical understanding and computational analysis. LQCD has become a standard tool in elementary particle physics, which can be solved by the hybrid Monte Carlo method. The calculation of force is most difficult part in the hybrid Monte Carlo method. This lecture gives the details of the force calculation in one-loop Symanzik improved action, Wilson fermion with clover term, asqtad fermion, HISQ fermion, rooted staggered fermion, smeared fermion, staggered Wilson fermion, overlap fermion and domain wall fermion. The even-odd precondition are also considered in these calculations.},
year = {2022}
}
TY - JOUR T1 - The Calculation of Force in Lattice Quantum Chromodynamics AU - Daming Li Y1 - 2022/02/15 PY - 2022 N1 - https://doi.org/10.11648/j.ajpa.20221001.12 DO - 10.11648/j.ajpa.20221001.12 T2 - American Journal of Physics and Applications JF - American Journal of Physics and Applications JO - American Journal of Physics and Applications SP - 8 EP - 23 PB - Science Publishing Group SN - 2330-4308 UR - https://doi.org/10.11648/j.ajpa.20221001.12 AB - Quantum chromodynamics (QCD) is the fundamental quantum field theory of quarks and gluons. To discuss it in a mathematically well-defined way, the theory has to be regularized by replacing space-time with a Euclidean lattice. This regularized theory, called lattice QCD (LQCD), has proven to be an efficient approach which allows for both theoretical understanding and computational analysis. LQCD has become a standard tool in elementary particle physics, which can be solved by the hybrid Monte Carlo method. The calculation of force is most difficult part in the hybrid Monte Carlo method. This lecture gives the details of the force calculation in one-loop Symanzik improved action, Wilson fermion with clover term, asqtad fermion, HISQ fermion, rooted staggered fermion, smeared fermion, staggered Wilson fermion, overlap fermion and domain wall fermion. The even-odd precondition are also considered in these calculations. VL - 10 IS - 1 ER -
Information
Email: