Non-renormalizability of the HMC algorithm

Journal of High Energy Physics

Volumn 2011, Issue 4, 2011, Pages

  Lüscher, Martin ^a   Schaefer, Stefan ^a  

^a CERN   (Switzerland)

Author keywords

Lattice QCD; Lattice quantum field theory; Renormalization regularization and renormalons

Indexed keywords

EID: 80053162194     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP04(2011)104     Document Type: Article

References (20)

1. J. Zinn-Justin, Renormalization and stochastic quantization, Nucl. Phys. B 275 (1986) 135.
2. J. Zinn-Justin and D. Zwanziger, Ward identities for the stochastic quantization of gauge fields, Nucl. Phys. B 295 (1988) 297.
3. A. Muñoz Sudupe and R.F. Alvarez-Estrada, Renormalization constants for the propagator of the stochastically quantized Yang-Mills field theory, Phys. Lett. B 164 (1985) 102.
4. A. Muñoz Sudupe and R.F. Alvarez-Estrada, β-function for Yang-Mills field theory in stochastic quantization, Phys. Lett. B 166 (1986) 186.
5. K. Okano, Background field method in stochastic quantization, Nucl. Phys. B 289 (1987) 109.
6. L. Baulieu and D. Zwanziger, QCD4 from a five-dimensional point of view, Nucl. Phys. B 581 (2000) 604 [hep-th/9909006].
7. L. Del Debbio, H. Panagopoulos and E. Vicari, Theta dependence of SU(N) gauge theories, JHEP 08 (2002) 044 [hep-th/0204125].
8. S. Schaefer, R. Sommer and F. Virotta, Investigating the critical slowing down of QCD simulations, PoS(LAT2009)032 [arXiv:0910.1465].
9. S. Schaefer, R. Sommer and F. Virotta, Critical slowing down and error analysis in lattice QCD simulations, Nucl. Phys. B 845 (2011) 93 [arXiv:1009.5228].
10. M. Lüscher, Topology, the Wilson flow and the HMC algorithm, PoS(Lattice 2010)015 [arXiv:1009.5877].
11. R. Sommer, A new way to set the energy scale in lattice gauge theories and its applications to the static force and ?s in SU(2) Yang-Mills theory, Nucl. Phys. B 411 (1994) 839 [hep-lat/9310022].
12. S. Duane, A.D. Kennedy, B.J. Pendleton and D. Roweth, Hybrid Monte Carlo, Phys. Lett. B 195 (1987) 216.
13. A.D. Kennedy and B. Pendleton, Cost of the generalised Hybrid Monte Carlo algorithm for free field theory, Nucl. Phys. B 607 (2001) 456 [hep-lat/0008020].
14. A.M. Horowitz, Stochastic quantization in phase space, Phys. Lett. B 156 (1985) 89.
15. A.M. Horowitz, The second order Langevin equation and numerical simulations, Nucl. Phys. B 280 (1987) 510.
16. A.M. Horowitz, A generalized guided Monte Carlo algorithm, Phys. Lett. B 268 (1991) 247.
17. M. Beccaria and G. Curci, The Kramers equation simulation algorithm. 1. Operator analysis, Phys. Rev. D 49 (1994) 2578 [hep-lat/9307007].
18. K. Jansen and C. Liu, Kramers equation algorithm for simulations of QCD with two flavors of Wilson fermions and gauge group SU(2), Nucl. Phys. B 453 (1995) 375 [Erratum ibid. B 459 (1996) 437] [hep-lat/9506020].
19. N.N. Bogoliubov and D.V. Shirkov, Introduction to the theory of quantized fields, Wiley-Interscience, New York U.S.A. (1959) [Intersci. Monogr. Phys. Astron. 3 (1959) 1].
20. M. Lüscher, Computational strategies in lattice QCD, lectures given at the Summer school on "Modern perspectives in lattice QCD", Les Houches France August 3-28 2009 [arXiv:1002.4232].