Abstract.
Four lectures about chiral symmetry and dynamical fermions in QCD. 1) Chiral symmetry in continuum QCD with an eye toward lattice simulations. 2) Lattice fermions with exact chiral symmetry: staggered fermions, fermions in five dimensions, chiral fermions in four dimensions. 3) A typical lattice simulation from beginning to end: the simulation algorithm, designing observables to measure some desired quantity, analyzing the data. 4) Recent lattice results relevant to chiral symmetry: a mini-review.
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References
T. DeGrand, C. DeTar, Lattice Methods for Quantum Chromodynamics (World Scientific, Singapore, 2006)
M. Gell-Mann, M. Levy, Nuovo Cim. 16, 705 (1960)
M. Gell-Mann, R.J. Oakes, B. Renner, Phys. Rev. 175, 2195 (1968)
J. Gasser, H. Leutwyler, Nucl. Phys. B 250, 465 (1985)
G. 't Hooft, Phys. Rev. D 14, 3432 (1976), Erratum-ibid. 18, 2199 (1978)
H.B. Nielsen, M. Ninomiya, Nucl. Phys. B 185, 20 (1981), Erratum-ibid. 195, 541 (1982); H.B. Nielsen, M. Ninomiya, Nucl. Phys. B 193, 173 (1981); H.B. Nielsen, M. Ninomiya, Phys. Lett. B 105, 219 (1981)
C.T.H. Davies, G.P. Lepage, F. Niedermayer, D. Toussaint, Nucl. Phys. Proc. Suppl. 140, 261 (2005) [arXiv:hep-lat/0409039]
For a discussion of this question, see S. Dürr, PoS LAT2005, 021 (2006) [arXiv:hep-lat/0509026]; Y. Shamir [arXiv:hep-lat/0607007], C. Bernard, M. Golterman, Y. Shamir [arXiv:hep-lat/0610003], and (my recommendation) S.R. Sharpe, PoS LAT2006, 022 (2006) [arXiv:hep-lat/0610094]
D.B. Kaplan, Phys. Lett. B 288, 342 (1992) [arXiv:hep-lat/9206013]
Y. Shamir, Nucl. Phys. B 406, 90 (1993) [arXiv:hep-lat/9303005]
D.B. Kaplan, M. Schmaltz, Phys. Lett. B 368, 44 (1996) [arXiv:hep-th/9510197]
P.H. Ginsparg, K.G. Wilson, Phys. Rev. D 25, 2649 (1982)
M. Lüscher [arXiv:hep-th/0102028]
H. Neuberger, Phys. Lett. B 417, 141 (1998) [arXiv:hep-lat/9707022]; H. Neuberger, Phys. Rev. Lett. 81, 4060 (1998) [arXiv:hep-lat/9806025]
N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, E. Teller, J. Chem. Phys. 21, 1087 (1953)
D.J.E. Callaway, A. Rahman, Phys. Rev. Lett. 49, 613 (1982); D.J.E. Callaway, A. Rahman, Phys. Rev. D 28, 1506 (1983)
S. Duane, J.B. Kogut, Phys. Rev. Lett. 55, 2774 (1985); S. Duane, J.B. Kogut, Nucl. Phys. B 275, 398 (1986)
S. Duane, A.D. Kennedy, B.J. Pendleton, D. Roweth, Phys. Lett. B 195, 216 (1987)
S.A. Gottlieb, W. Liu, D. Toussaint, R.L. Renken, R.L. Sugar, Phys. Rev. D 35, 2531 (1987)
T.A. DeGrand (MILC Collaboration), Phys. Rev. D 69, 014504 (2004) [arXiv:hep-lat/0309026]
W.-J. S. Lee, S.R. Sharpe, Phys. Rev. D 68, 054510 (2003) [arXiv:hep-lat/0306016]
C. Aubin, C. Bernard, Phys. Rev. D 68, 034014 (2003) [arXiv:hep-lat/0304014]
S.R. Sharpe [arXiv:hep-lat/0607016]
This is an enormous subject. Some references I have found valuable include H. Leutwyler, A. Smilga, Phys. Rev. D 46, 5607 (1992) and the reviews by P.H. Damgaard, Nucl. Phys. Proc. Suppl. 106, 29 (2002) [arXiv:hep-lat/0110192]; M.A. Stephanov, J.J.M. Verbaarschot, T. Wettig [arXiv:hep-ph/0509286]
T. DeGrand, Z. Liu, S. Schaefer, Phys. Rev. D 74, 094504 (2006), Erratum-ibid. 74, 099904 (2006) [arXiv:hep-lat/0608019]
M. Jamin, Phys. Lett. B 538, 71 (2002) [arXiv:hep-ph/0201174]
G. 't Hooft, Nucl. Phys. B 75, 461 (1974)
A. Armoni, M. Shifman, G. Veneziano, Phys. Rev. Lett. 91, 191601 (2003) [arXiv:hep-th/0307097]; A. Armoni, M. Shifman, G. Veneziano, Nucl. Phys. B 667, 170 (2003) [arXiv:hep-th/0302163]
A. Armoni, M. Shifman, G. Veneziano, Phys. Lett. B 579, 384 (2004) [arXiv:hep-th/0309013]
A. Armoni, M. Shifman, G. Veneziano, Phys. Rev. D 71, 045015 (2005) [arXiv:hep-th/0412203]
N.M. Davies, T.J. Hollowood, V.V. Khoze, M.P. Mattis, Nucl. Phys. B 559, 123 (1999) [arXiv:hep-th/9905015]
T. DeGrand, R. Hoffmann, S. Schaefer, Z. Liu, Phys. Rev. D 74, 054501 (2006) [arXiv:hep-th/0605147]
A. Armoni, G. Shore, G. Veneziano, Nucl. Phys. B 740, 23 (2006) [arXiv:hep-ph/0511143]
S. Capitani, M. Lüscher, R. Sommer, H. Wittig (ALPHA Collaboration), Nucl. Phys. B 544, 669 (1999) [arXiv:hep-lat/9810063]
M. Della Morte, R. Frezzotti, J. Heitger, J. Rolf, R. Sommer, U. Wolff (ALPHA Collaboration), Nucl. Phys. B 713, 378 (2005) [arXiv:hep-lat/0411025]
W.J. Marciano, Phys. Rev. Lett. 93, 231803 (2004) [arXiv:hep-ph/0402299]
W.M. Yao et al. (Particle Data Group), J. Phys. G 33, 1 (2006)
C. Bernard et al. [arXiv:hep-lat/0611024]
M. Della Morte, R. Hoffmann, F. Knechtli, J. Rolf, R. Sommer, I. Wetzorke, U. Wolff (ALPHA Collaboration), Nucl. Phys. B 729, 117 (2005) [arXiv:hep-lat/0507035]
T. Ishikawa et al. (CP-PACS Collaborations), PoS LAT2005, 057 (2006) [arXiv:hep-lat/0509142]
M. Göckeler, R. Horsley, A.C. Irving, D. Pleiter, P.E.L. Rakow, G. Schierholz, H. Stuben (QCDSF Collaboration), Phys. Lett. B 639, 307 (2006) [arXiv:hep-ph/0409312]
D. Becirevic et al., PoS LAT2005, 079 (2006) [arXiv:hep-lat/0509091]
S.R. Sharpe, N. Shoresh, Phys. Rev. D 62, 094503 (2000) [arXiv:hep-lat/0006017]
S.R. Sharpe, Phys. Rev. D 56, 7052 (1997), Erratum-ibid. 62, 099901 (2000) [arXiv:hep-lat/9707018]
P.H. Damgaard, K. Splittorff, Phys. Rev. D 62, 054509 (2000) [arXiv:hep-lat/0003017]
C. Aubin, C. Bernard, Nucl. Phys. Proc. Suppl. 129, 182 (2004) [arXiv:hep-lat/0308036]
S. Prelovsek, Phys. Rev. D 73, 014506 (2006) [arXiv:hep-lat/0510080]
C. Aubin et al., Phys. Rev. D 70, 094505 (2004) [arXiv:hep-lat/0402030]
E.B. Gregory, A.C. Irving, C.C. McNeile, S. Miller, Z. Sroczynski, PoS LAT2005, 027 (2006) [arXiv:hep-lat/0510066]
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DeGrand, T. Chiral symmetry and lattice QCD. Eur. Phys. J. Spec. Top. 152, 1–27 (2007). https://doi.org/10.1140/epjst/e2007-00375-4
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DOI: https://doi.org/10.1140/epjst/e2007-00375-4