BUSSTEPP 2002
Lattice Methods in Field Theory

• slides used in the lectures (updated to include the hand-written transparencies)
• Problems with solutions

Preliminary Reading

• Standard textbook quantum field theory, including functional methods. Section 10.5 of Cheng & Li (Gauge Theory of Elementary Particle Physics, OUP) mentions lattice gauge theory and colour confinement.
• Phenomenology from Lattice QCD: review by CT Sachrajda at Lepton-Photon 2001 in Rome, concentrating on the physics of beauty and strangeness.
• Review by RD Kenway at ICHEP 2000 in Osaka. Written for the general high energy physics community (theory and experiment), this concentrates on progress in lattice QCD during the previous two years and, particularly, its impact on phenomenology. This should help show you the place of lattice QCD in contemporary particle physics.

From the Summer School lectures below, I recommend the first three, by Sachrajda, Sharpe and Munster/Walzl to get you started. At BUSSTEPP I will not try to survey the whole of lattice field theory. I will not assume any previous knowledge of the subject. The references here cover far more than we will have time to explore.

Some other Summer School lectures

• Lattice Phenomenology (C Sachrajda, Benasque Summer School, Spain, 2000). First three sections describe the application of lattice simulations to particle physics phenomenology. Section 4 onwards is devoted mostly to B physics. You might also like to consult Lattice Simulations and Effective Theories (C Sachrajda, Adv School on Eff Theories, Almunecar, Spain, 1995, hep-lat/9605027): introduction to the lattice formulation of quantum field theory, with applications to phenomenology (mostly b physics).
• Phenomenology from the Lattice (S Sharpe, TASI 1994, hep-ph/9412243): essentials of lattice calculations and illustration of application to Kaon B parameter.
• Lattice Gauge Theory - A Short Primer (G Munster and M Walzl, ZUOZ 2000): introduction to the foundations and methods of lattice gauge theory (starting from the quantum mechanical path integral and moving on through functional integrals, Euclidean field theory and discretisation).
• From Monte Carlo Integration to Lattice QCD (M di Pierro): highly practical introduction to Monte Carlos integration and its application to lattice QCD. Includes example programs.
• Lattice QCD (C Davies): Lectures from the 2001 Scottish Universities' Summer School concentrating on applications to heavy quark physics (the topic of that school).
• Nonperturbative Quantum Field Theory on the Lattice (T DeGrand, TASI 1996, hep-th/9610132): introduction to lattice methods for nonperturbative quantum field theory, with emphasis on QCD.
• Introduction to lattice QCD (R Gupta, Les Houches Summer School, 1997, hep-lat/9807028). Topics covered: scope of LQCD calculations, discretization, improvement, confinement and strong coupling expansions, phase transitions in the lattice theory, lattice operators, statistical and systematic errors, phenomenology.
• Advanced lattice QCD (M Luscher, Les Houches Summer School, 1997, hep-lat/9802029). Covers improvement, chiral symmetry on the lattice and non-perturbative renormalisation.
• Chiral gauge theories revisited (M Luscher, Int School of Subnuclear Phys, Erice, Italy, 2000, hep-th/0102028). The author has played a vital role in recent developments in putting chiral gauge theories on the lattice.
• From actions to answers. TASI Summer School, Boulder, Colorado, 1989. Eds: T DeGrand and D Toussaint (World Scientific, Singapore, 1990). Contains several sets of lectures on lattice field theory.

Bibliography

• M Creutz, Quarks, Gluons and Lattices (CUP 1983)
• I Montvay and G Munster, Quantum Fields on a Lattice (CUP 1994)
• HJ Rothe, Lattice Gauge Theories: an Introduction (World Scientific 1992)
• For annual overviews see the proceedings of the International Symposia on Lattice Field Theory: 2002, 2001, 2000

Creutz is the granddaddy of lattice calculations: I have heard it said that he did the first tiny lattice simulations on a Commodore PET (if you remember those). His and Rothe's books are quite readable. Montvay and Munster's book is very thorough and hence less digestible