Project IV 2026-27


Lattice QCD

Arthur Lipstein

Description

Quantum Chromodynamics (QCD) describes the interaction of quarks and gluons. At low energies the theory becomes strongly coupled making it challenging to do calculations, but can be successfully described by putting it on a lattice. The goal of this project will be to derive the confining potential between a quark and anti-quark from first principles using the lattice formulation, both analytically and numerically. In more detail, students will learn about

  • Yang-Mills theory in the continuum
  • Wilson loops, lattice gauge theory, and confinement
  • numerical methods for lattice simulations
  • Using the above tools, students can then write code to carry out lattice QCD calculations using any computer language of their choice. Students will have the opportunity to explore other related directions if time permits. For example, they can learn about how to describe dynamical quarks or supersymmetry on the lattice.

    Mode of Operation and Evidence of Learning

    The project will revolve around learning through reading and programming with focus on the underlying theory and the development of conceptual understanding. Students will demonstrate their understanding by solving relevant problems, writing code to carry out lattice simulations, and clearly communicating it in both written and oral formats.

    Suggested Pre-requisites

    Quantum Mechanics III

    Suggested Co-requisites

    Advanced Quantum Theory IV

    Resources

  • "Quarks, Gluons, and Lattices" by Creutz
  • Srednicki's book book on Quantum Field Theory
  • This classic paper by Creutz