Lattice Field Theory

PD Dr. Stephan Dürr / Summer 2024

Content Summary

• Reminder on statistical mechanics
• Path integral quantization
• Scalar field theory on the lattice
• Lattice perturbation theory
• Monte Carlo methods
• Gauge theories on the lattice
• Correlated datasets
• Glueball physics
• Strong coupling expansion
• Continuum limit and phase transitions
• Fermions on the lattice
• Chiral symmetry on the lattice
• Hybrid Monte Carlo
• Hadron spectroscopy
• Electroweak matrix elements
• Nuclear physics topics

Suggested Books

• M. Creutz, "Quarks, gluons and lattices", Cambridge University Press, 1983/1997.
• I. Montvay and G. Münster, "Quantum fields on a lattice", Cambridge University Press, 1994.
• H. Rothe, "Lattice Gauge Theories an Introduction", World Scientific Lecture Notes in Physics vol 59, 1997.
• J. Smit, "Introduction to Quantum Fields on a Lattice", Cambridge University Press, 2002.
• T. De Grand and C. De Tar, "Lattice Methods for Quantum Chromodynamics", World Scientific, Singapore, 2006.
• C. Gattringer and C.B. Lang, "Quantum Chromodynamics on the Lattice", Springer-Verlag, Berlin, Heidelberg, 2010.
• F. Knechtli, M. Günther and M. Peardon, Lattice Quantum Chromodynamics, Springer-Verlag, Berlin, Heidelberg, 2016.

Suggested Articles

• M. Creutz and B. Freedman, "A statistical approach to quantum mechanics", Annals Phys. 132 (1981) 427.
• J.B. Kogut, "A review on the lattice gauge theory approach to Quantum Chromodynamics", Rev. Mod. Phys. 55 (1983) 775.
• R. Gupta, "Introduction to Lattice QCD", hep-lat/9807028 .
• G.P. Lepage, "Lattice QCD for novices", hep-lat/0506036 .
• M. DiPierro, "An Algorithmic approach to quantum field theory" hep-lat/0509013 .
• C. Morningstar, "The Monte Carlo method in quantum field theory", hep-lat/0702020 .
• I. Montvay, "Monte Carlo methods in quantum field theory", arXiv:0705.4356 .
• M. Lüscher, "Computational strategies in Lattice QCD", arXiv:1002.4232 .
• L. Lellouch, "Flavor physics and Lattice Quantum Chromodynamics", arXiv:1104.5484 .
• Z. Fodor, Ch. Hoelbling, "Light hadron masses from Lattice QCD", arXiv:1203.4789 .
• M. Hanada, "Markov Chain Monte Carlo for dummies", arXiv:1808.08490.

Scholarpedia Articles

• path integrals by Jean Zinn-Justin
• phi-to-the-fourth by Ulli Wolff
• lattice field theory by Gernot Münster
• lattice gauge theory by Peter Weisz and Pushan Majumdar
• gauge theories by Gerard 't Hooft
• gauge invariance by Jean Zinn-Justin and Riccardo Guida
• chiral perturbation theory by Heinrich Leutwyler
• nuclear forces by Ruprecht Machleidt

Organization Details