Lattice methods and effective field theory

Abstract

Lattice field theory is a non-perturbative tool for studying properties of strongly interacting field theories, which is particularly amenable to numerical calculations and has quantifiable systematic errors. In these lectures we apply these techniques to nuclear Effective Field Theory (EFT), a non-relativistic theory for nuclei involving the nucleons as the basic degrees of freedom. The lattice formulation of [1,2] for so-called pionless EFT is discussed in detail, with portions of code included to aid the reader in code development. Systematic and statistical uncertainties of these methods are discussed at length, and extensions beyond pionless EFT are introduced in the final Section.

Lectures prepared for the ECT* Doctoral Training Program, "Computational Nuclear Physics", April 13 - May 22, 2015. Submitted to Lect. Notes Phys., "An advanced course in computational nuclear physics: Bridging the scales from quarks to neutron stars", Morten Hjorth-Jensen, Maria Paola Lombardo, Ubirajara van Kolck, Editors. Code to be included online with published version

References in corpus (20)

• Many-Body Physics with Ultracold Gases
• Theory of ultracold Fermi gases
• Chiral effective field theory and nuclear forces
• Nonrelativistic conformal field theories
• Toward the excited meson spectrum of dynamical QCD
• Light Nuclei and Hypernuclei from Quantum Chromodynamics in the Limit of SU(3) Flavor Symmetry
• Nuclear Physics from Lattice QCD
• Resonances in coupled $\pi K,\eta K$ scattering from lattice QCD
• Hyperon-Nucleon Scattering from Fully-Dynamical Lattice QCD
• Multichannel one-to-two transition amplitudes in a finite volume
• Lattice Simulations for Light Nuclei: Chiral Effective Field Theory at Leading Order
• Universal properties of a trapped two-component Fermi gas at unitarity
• n-Boson Energies at Finite Volume and Three-Boson Interactions
• Baryon-Baryon Interactions in the Flavor SU(3) Limit from Full QCD Simulations on the Lattice
• High Statistics Analysis using Anisotropic Clover Lattices: (II) Three-Baryon Systems
• The $\pi \pi \to \pi {\gamma }^{\star }$ amplitude and the resonant $\rho \to \pi {\gamma }^{\star }$ transition from lattice QCD
• Magnetic moments of light nuclei from lattice quantum chromodynamics
• Signal/noise enhancement strategies for stochastically estimated correlation functions
• Sign problems, noise, and chiral symmetry breaking in a QCD-like theory
• The Hoyle state in Nuclear Lattice EFT

Cited by in corpus (3)

• A Guided Tour of Ab Initio Nuclear Many-Body Theory
• Structure Factors of Neutron Matter at Finite Temperature
• From few to many body degrees of freedom