Lattice Field Theory

A strongly abridged version of the below, from 2006, in slide format .

Lecturer: Mikko Laine
Time: Wed 10-12, Fri 14-16, starting 15.10.2003.
Place: D6-135.
Background: Statistical physics / particle physics / computational science.
Literature: * J.Smit, Introduction to Quantum Fields on a Lattice.
* H.J.Rothe, Lattice Gauge Theories, an Introduction.
* I.Montvay and G.Muenster, Quantum Fields on a Lattice.
Schedule: 15.10.: Spin models: Physics background. Definition. Basic thermodynamics. Solution for d=1 Ising. (p.1-5)
17.10.: Spin models: Global symmetries. Symmetry breaking. Phase transitions. (p.6-10)
22.10.: Discretised field theory vs spin models. Fourier analysis on the lattice. (p.11-15)
24.10.: Weak coupling expansion. Wick's theorem. Propagator. (p.16-20)
29.10.: An example of a 1-loop computation. (p.21-25)
31.10.: No lecture.
05.11.: "Strong coupling expansion" - hopping parameter expansion. (p.26-30)
07.11.: Monte Carlo integration. Random numbers. Importance sampling. (p.31-35)
12.11.: Importance sampling (continued). Update algorithms. (p.36-40)
14.11.: Reliable error estimation: autocorrelation time; jackknife, bootstrap. Reweighting. (p.41-45)
19.11.: An example of a simulation: d = 2 Ising. (p.46-55)
21.11.: Approach to the continuum limit. The outcome for d = 3, d = 4 Ising universality class. (p.56-60)
26.11.: Euclidean vs Minkowskian spacetime. Quantum statistical mechanics & field theory. (p.61-65)
28.11.: Gauge symmetry. Pure gauge theory on the lattice. Group integration. (p.66-70)
03.12.: Weak coupling expansion. Continuum limit. Asymptotic freedom. (p.71-75)
05.12.: Strong coupling expansion. Wilson loop. Confinement. (p.76-80)
10.12.: Gauge + Higgs theory. "Spontaneous gauge symmetry breaking". (p.81-85)
12.12.: Fermions. Naive discretisation. Propagator. The fermion "doubling" problem. (p.86-90)
17.12.: Wilson fermions. Spectral representation of propagator. Boundary conditions. (p.91-95)
19.12.: No lecture.
07.01.: Overview of contemporary directions in lattice gauge field theories. (p.96-100)
09.01.: QCD: properties of pure gauge theory; "QCD scale". (p.101-105)
15.01.: QCD: global symmetries, symmetry breaking pattern. (p.106-110)
17.01.: QCD: Goldstone phenomenon, low-energy effective theories. (p.111-115)
21.01.: QCD: spectroscopy, directly: hadronic correlation functions; problem of scale hierarchies. (p.116-120)
23.01.: QCD: spectroscopy, indirectly: matching to low-energy effective theories. (p.121-125)
28.01.: QCD: weak matrix elements. (p.126-130)
30.01.: QCD: finite temperature physics, phase diagram. (p.131-135)
04.02.: QCD: finite baryon density; "sign problem". (p.136-140)
06.02.: No lecture.