Kenneth Wilson and lattice QCD

Abstract

We discuss the physics and computation of lattice QCD, a space-time lattice formulation of quantum chromodynamics, and Kenneth Wilson's seminal role in its development. We start with the fundamental issue of confinement of quarks in the theory of the strong interactions, and discuss how lattice QCD provides a framework for understanding this phenomenon. A conceptual issue with lattice QCD is a conflict of space-time lattice with chiral symmetry of quarks. We discuss how this problem is resolved. Since lattice QCD is a non-linear quantum dynamical system with infinite degrees of freedom, quantities which are analytically calculable are limited. On the other hand, it provides an ideal case of massively parallel numerical computations. We review the long and distinguished history of parallel-architecture supercomputers designed and built for lattice QCD. We discuss algorithmic developments, in particular the difficulties posed by the fermionic nature of quarks, and their resolution. The triad of efforts toward better understanding of physics, better algorithms, and more powerful supercomputers have produced major breakthroughs in our understanding of the strong interactions. We review the salient results of this effort in understanding the hadron spectrum, the Cabibbo-Kobayashi-Maskawa matrix elements and CP violation, and quark-gluon plasma at high temperatures. We conclude with a brief summary and a future perspective.

52 pages, 16 figures, to appear in Journal of Statistical Physics

References in corpus (25)

• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• The order of the quantum chromodynamics transition predicted by the standard model of particle physics
• The equation of state in (2+1)-flavor QCD
• The QCD transition temperature: results with physical masses in the continuum limit
• Ab-initio Determination of Light Hadron Masses
• Nuclear Force from Lattice QCD
• Ab initio calculation of the neutron-proton mass difference
• A calculation of the bulk viscosity in SU(3) gluodynamics
• Freeze-out Conditions in Heavy Ion Collisions from QCD Thermodynamics
• Freeze-out parameters from electric charge and baryon number fluctuations: is there consistency?
• Adaptive multigrid algorithm for the lattice Wilson-Dirac operator
• Precise Measurements of Direct CP Violation, CPT Symmetry, and Other Parameters in the Neutral Kaon System
• Lattice QCD at the physical point: light quark masses
• Electromagnetic mass splittings of the low lying hadrons and quark masses from 2+1 flavor lattice QCD+QED
• The B -> pi l nu semileptonic form factor from three-flavor lattice QCD: A model-independent determination of |V(ub)|
• Local coherence and deflation of the low quark modes in lattice QCD
• Stochastic quantization at finite chemical potential
• Relativistic Heavy Quark Effective Action
• Measurement of the pseudorapidity and centrality dependence of the transverse energy density in PbPb collisions at sqrt(s[NN]) = 2.76 TeV
• Finite density phase transition of QCD with $N_f=4$ and $N_f=2$ using canonical ensemble method
• Nuclear Force from Lattice QCD
• Neutral B-meson mixing from three-flavor lattice QCD: Determination of the SU(3)-breaking ratio ξ
• Automatic O(a) improvement for twisted-mass QCD in the presence of spontaneous symmetry breaking
• Running of the SF-coupling with four massless flavours
• Automatic O$(a)$ improvement for twisted-mass QCD

Cited by in corpus (1)

• Measurement of Target and Double-spin Asymmetries for the $\vec{e}\vec{p}\to e{\pi }^{+}(n)$ Reaction in the Nucleon Resonance Region at Low $Q^2$