Abstract
When introducing the QCD action on the lattice we had to discretize the derivative terms that show up in the continuum action. It was pointed out then that any discretization, e.g., symmetric differences for the first derivative in the fermion action, gives rise to discretization effects. Typically the discretization effects are of (a) for fermions and of (a 2) for the gauge fields. These disappear only in the continuum limit when the lattice spacing it a is sent to zero. Performing the continuum limit is, however, a nontrivial task. As one decreases a, the number of lattice points has to increase, such that the physical volume remains constant (ideally one would first send the number of lattice points to infinity before sending a to zero). Thus in a numerical simulation one always works with finite a and the discretization errors have to be dealt with, e.g., by including them in the extrapolation to vanishing a.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
K. Symanzik: Nucl. Phys. B 226, 187 (1983)
K. Symanzik: Nucl. Phys. B 226, 205 (1983)
M. Lüscher and P. Weisz: Commun. Math. Phys. 97, 59 (1985)
M. Lüscher and P. Weisz: Commun. Math. Phys. 98, 433 (1985)
B. Sheikholeslami and R. Wohlert: Nucl. Phys. B 259, 572 (1985)
M. Lüscher, S. Sint, R. Sommer, and P. Weisz: Nucl. Phys. B 478, 365 (1996)
M. Lüscher: in Probing the Standard Model of Particle Interactions, Proceedings Les Houches 1997, edited by R. Gupta, A. Morel, E. de Rafael, and F. David, Vol. 1 (Elsevier, Amsterdam 1998)
G. Curci, P. Menotti, and G. Paffuti: Phys. Lett. B 130, 205 (1983)
G. Curci, P. Menotti, and G. Paffuti: Phys. Lett. B 135, 516 (1984)
R. Wohlert (unpublished) DESY 87–069 (1987)
M. Lüscher and P. Weisz: Nucl. Phys. B 479, 429 (1996)
G. P. Lepage and P. B. Mackenzie: Phys. Rev. D 48, 2250 (1993)
T. DeGrand and C. DeTar: Lattice Methods for Quantum Chromodynamics (World Scientific, Singapore 2006)
K. Symanzik: Nucl. Phys. B 190, 1 (1981)
M. Lüscher: Nucl. Phys. B 254, 252 (1985)
M. Lüscher, R. Narayanan, P. Weisz, and U. Wolff: Nucl. Phys. B 384, 168 (1992)
S. Sint: Nucl. Phys. B 421, 135 (1994)
S. Sint: Nucl. Phys. B 451, 416 (1995)
M. Lüscher et al.: Nucl. Phys. B 491, 323 (1997)
R. G. Edwards, U. M. Heller, and T. R. Klassen: Nucl. Phys. (Proc. Suppl.) 63, 847 (1998)
K. Jansen and R. Sommer: Nucl. Phys. B 530, 185 (1998)
W. Bietenholz and U.-J. Wiese: Nucl. Phys. B 464, 319 (1996)
K. G. Wilson and J. Kogut: Phys. Rep. 12C, 76 (1974)
K. G. Wilson: Rev. Mod. Phys. 47, 773 (1975)
P. Hasenfratz: in Advanced School on Non-Perturbative Quantum Field Physics: Peniscola, Spain 2–6 June 1997, edited by M. Asorey and A. Dobado, p. 137 (World Scientific, Singapore 1998)
P. Hasenfratz and F. Niedermayer: Nucl. Phys. B 414, 785 (1994)
T. DeGrand, A. Hasenfratz, P. Hasenfratz, and F. Niedermayer: Nucl. Phys. B 454, 587 (1995)
T. DeGrand, A. Hasenfratz, P. Hasenfratz, and F. Niedermayer: Nucl. Phys. B 454, 615 (1995)
M. Blatter and F. Niedermayer: Nucl. Phys. B 482, 286 (1996)
P. Hasenfratz et al.: Int. J. Mod. Phys. C12, 691 (2001)
C. Gattringer: Phys. Rev. D 63, 114501 (2001)
C. B. Lang and T. K. Pany: Nucl. Phys. B 513, 645 (1998)
P. Hasenfratz et al.: Nucl. Phys. B (Proc. Suppl.) 94, 627 (2001)
P. Hasenfratz et al.: Nucl. Phys. B (Proc. Suppl.) 106, 799 (2002)
P. Hasenfratz et al.: Nucl. Phys. B 643, 280 (2002)
S. Hauswirth: Ph.D. thesis, Universität Bern, Switzerland (2002)
T. Jörg: Ph.D. thesis, Universität Bern, Switzerland (2002)
C. Gattringer: Nucl. Phys. B (Proc. Suppl.) 119, 122 (2002)
C. Gattringer et al. [BGR (Bern-Graz-Regensburg) collaboration]: Nucl. Phys. B 677, 3 (2004)
P. Hasenfratz, V. Laliena, and F. Niedermayer: Phys. Lett. B 427, 125 (1998)
P. Hasenfratz: Nucl. Phys. B 525, 401 (1998)
C. Gattringer, I. Hip, and C. B. Lang: Nucl. Phys. B 597, 451 (2001)
C. Gattringer et al.: Phys. Rev. D 79, 054501 (2009)
P. H. Ginsparg and K. G. Wilson: Phys. Rev. D 25, 2649 (1982)
C. Gattringer and M. Pak: PoS LATTICE2007, 081 (2007)
P. Hasenfratz, F. Niedermayer, and R. von Allmen: JHEP 0610, 010 (2006)
K. Fujikawa: Phys. Rev. Lett. 42, 1195 (1979)
K. Fujikawa: Phys. Rev. D 21, 2848 (1980)
P. Hasenfratz and M. Bissegger: Phys. Lett. B 613, 57 (2005)
P. Hasenfratz and R. von Allmen: JHEP 0802, 079 (2008)
C. Gattringer and M. Pak: Nucl. Phys. B 801, 353 (2008)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Gattringer, C., Lang, C.B. (2010). Symanzik improvement and RG actions. In: Quantum Chromodynamics on the Lattice. Lecture Notes in Physics, vol 788. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01850-3_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-01850-3_9
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-01849-7
Online ISBN: 978-3-642-01850-3
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)