Project IV 2023-24

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 (chapters 54,69, and 71 of Srednicki's book)
  • the beta function and asympotic freedom (chapters 29 and 73 of Srednicki's book)
  • path integrals and statistical mechanics (chapter 3 of Creutz's book "Quarks, Gluons, and Lattices")
  • Wilson loops, lattice gauge theory, and confinement (chapter 82 of Srednicki's book, chapter 10 of Creutz's book)
  • numerical methods for lattice simulations (chapters 18 and 19 of Creutz's book)

    • Using the above tools, students can then write code to carry out lattice QCD calculations using any computer language of their choice, with the goal of reproducing some of the results in this classic paper. Students will have the opportunity to explore other related directions if time permits. For example, they can learn about how to describe dynamical quarks on the lattice.

    Suggested Pre-requisites

    Quantum Mechanics III

    Suggested Co-requisites

    Advanced Quantum Theory IV