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.