Special Topics 694: Introduction to Lattice Field Theory
Course overview and description
This introductory course is for graduate students in nuclear, particle, and condensed matter theory (or experiment) or for anyone interested in field theory more generally. The course will bridge quantum field theory and statistical physics and will emphasise two key insights:
- 1. many quantum field theories in D-dimensions are equivalent to the classical thermodynamics of a statistical system in (D+1)-dimensions;
- 2. the lattice provides our only rigorous (at least in a physicist's sense!) nonperturbative definition of a quantum field theory.
The course, listed in the Schedule of Classes as Advanced Topics in High Energy II, will take place on Mondays and Wednesdays at 10:20-11:40am in Serin room 106 (SRN-106). The first lecture will take place on Wednesday 20th January.
There are no formal prerequisites, but some familiarity with the path integral would be helpful.
There will be no lectures on:
- Wednesday 27th January (I'm away)
- Monday 14th March and Wednesday 16th March (Spring break)
- Monday 21st March and Wednesday 23rd March (I'm away)
Instructor: Chris Monahan
Office: Serin 208W
Office hours will be on Mondays 14:15 to 15:15
Course format and assessmentThere will be five homeworks, the first of which will be handed out at the end of lecture on Monday 25th January. One assignment will be an eight minute presentation on a topic, taken from the course, of your choice. Another will be an essay. The homework schedule is:
- Problem Set 1. Monday 25th January. Due Wednesday 3rd February.
- Problem Set 2. Monday 8th February. Due Wednesday 17th February.
- Essay. Monday 22nd February. Due Monday 7th March.
- Presentation. Wednesday 9th March. Due Monday 28th March.
- Problem Set 3. Monday 28th March. Due Wednesday 6th April.
- Problem sets: 30%
- Essay: 15%
- Presentation: 20%
- Final project: 35%
The course will cover the following topics, although the exact content may evolve as the course progresses:
- Lattice and statistical scalar field theory
- A (very) quick reminder of statistical mechanics
- The path integral in quantum mechanics and quantum field theory
- Scalar field theories
- Phase transitions and the continuum limit
- Renormalisation, the block-spin transformation and the renormalisation group
- Statistical approaches to the path integral
- Markov chains and stochastic sampling
- Monte Carlo algorithms for scalar field theories
- Data analysis and systematic uncertainties
- Lattice gauge theory
- Yang-Mills theory on the lattice: the Wilson action
- Analytic approaches: strong and weak coupling expansions
- The Wilson loop, confinement and asymptotic freedom
- Fermions on the lattice and the doubling problem
- Chiral symmetry and anomalies
- Symanzik improvement
- Effective field theories on the lattice
- Contemporary research directions in lattice QCD
Please feel free to email me, chris.monahan'at'rutgers.edu, if you have questions.
TextbooksI will not be following a particular textbook. However, you may (or may not) find the following textbooks helpful:
- Quantum chromodynamics on the lattice, C. Gattringer and C.B. Lang, Springer (2010);
- Lattice methods for quantum chromodynamics, T. DeGrand and C. DeTar, World Scientific (2006);
- Introduction to quantum fields on a lattice, J. Smit, Cambridge (2002);
- Quantum field on a lattice, I. Montvay and G. Munster, Cambridge (1994);
- Quarks, gluons and lattices, M. Creutz, Cambridge (1983);
- A guide to Monte Carlo simulations in statistical physics, D.P. Landau and K. Binder, Cambridge (2015);
- Monte Carlo methods in statistical physics, M.E.J. Newman and G.T. Barkema, Oxford (1999);
- Monte Carlo simulation in statistical physics, K. Binder and D.W. Heermann, Springer (1997).
- Confinement, chiral symmetry, and the lattice, M. Creutz, 2012;
- The Monte Carlo method in quantum field theory, C. Morningstar, 2007;
- From Monte Carlo integration to lattice quantum chromo dynamics, M. Di Pierro, 2001;
- Introduction to lattice QCD, R. Gupta, 1998;
- Lattice QCD for Small Computers, G.P. Lepage, 1994.
If you have a disability, please contact me so that we can make any necessary arrangements. See here for more information.