## Introduction to Lattice Field Theory

Special Topics 694: Introduction to Lattice Field Theory

[Image taken from xkcd (where else?).]

The course webpage is here and the graduate course homepage here.

### 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
20^{th} January.

There are no formal prerequisites, but some familiarity with the path integral would be helpful.

### Lecture cancellations

There will be no lectures on:

- Wednesday 27
^{th}January (I'm away) - Monday 14
^{th}March and Wednesday 16^{th}March (Spring break) - Monday 21
^{st}March and Wednesday 23^{rd}March (I'm away)

### Contact details

Instructor: Chris Monahan

Office: Serin 208W

Email: chris.monahan'at'rutgers.edu

Office hours will be on Mondays 14:15 to 15:15

### Course format and assessment

There will be five homeworks, the first of which will be handed out at the end of lecture on Monday 25^{th}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 25
^{th}January. Due Wednesday 3^{rd}February. - Problem Set 2. Monday 8
^{th}February. Due Wednesday 17^{th}February. - Essay. Monday 22
^{nd}February. Due Monday 7^{th}March. - Presentation. Wednesday 9
^{th}March. Due Monday 28^{th}March. - Problem Set 3. Monday 28
^{th}March. Due Wednesday 6^{th}April.

**at the beginning**of the lecture on the due date. Late homeworks will score zero, with no exceptions. If there are particularly special or unusual circumstances, or you require further accommodation (see the comments on Accessibility below), please get in touch with me in advance. There will not be a final exam, but a final project. This final project will be an extended homework-like project, which will be submitted as a short paper, written in LaTeX and typeset according to Physical Review style. These assessments should not only improve your understanding of lattice field theory, but also develop your presentation and scientific writing skills as part of your training as a professional researcher. Assessment weighting will be:

- Problem sets: 30%
- Essay: 15%
- Presentation: 20%
- Final project: 35%

**will**affect your grade.

### Topics

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.

### Textbooks

I 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).

*Field theory: a modern primer*, P. Ramond, Addison-Wesley (1990)

*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.

### Accessibility

If you have a disability, please contact me so that we can make any necessary arrangements. See here for more information.