TCM308 Lattice Field Theory



o Lecturer: Kari Rummukainen
o Lectures: 2h/week, Mon 10-12 A315 (HIP seminar room)

o Excercise: Mon 12-14 A315 (HIP seminar room)

o Home exam! Return by 15.12 14.00
exam answers

o Description: Lattice regularisation is the most robust way to define quantum field theories; it is the only known non-perturbative and gauge invariant regularisation. It also offers an avenue for numerical simulations of QFTs. This course gives an overview of the quantum fields on the lattice, including theoretical properties and also gives an introduction to numerical methods.
o Contents: Spin systems, path integral on the lattice, free scalar fields, gauge fields, lattice fermions, doublers, weak and strong coupling expansions (low- and high temperature expansions), lattice Monte Carlo methods, error analysis (to be updated)
o Requirements: Quantum Mechanics II and statistical physics. Basic knowledge of quantum field theories (introduction to quantum field theory) is recommended.

Lecture notes
o Exercises:
o Excercise 1. Discussed 18.9 and 25.9.
o Excercise 2. Discussed 25.9 and 2.10.
o Excercise 3. Discussed 2.10 and 9.10.
o Excercise 4. Discussed 30.10 and 6.11.
o Excercise 5. Discussed 6.11 and 13.11.
o Excercise 6. Discussed 20.11 and 27.11.
o Excercise 7. Discussed 27.11 and 4.12.
o
o Home exam! Return by 15.12 14.00

o Textbooks and other course material:

  • I. Montvay, G. Münster: Quantum Fields on a Lattice, Cambridge Univ. Press
  • H. Rothe: Lattice gauge theories: an Introduction, World Scientific 1992
  • J. Smit: Introduction to Quantum Fields on a Lattice, Cambridge lecture notes in Physics
  • M. Creutz: Quarks, Gluons and Lattices, Cambridge Univ. Press 1983. Introduction to field theory on the lattice, not much about simulation methods.