Lattice Quantum Chromodynamics for Pedestrians
QuantumChromoDynamics Pure gauge theory Lettuce Field Theory An introduction Christian B. Lang Christian B. Lang Lattice QCD for Pedestrians QuantumChromoDynamics Pure gauge theory Lattice Quantum Field Theory An introduction Christian B. Lang Christian B. Lang Lattice QCD for Pedestrians QuantumChromoDynamics Pure gauge theory Christian B. Lang Lattice QCD for Pedestrians Continuum QCD QuantumChromoDynamics Quantization Pure gauge theory Lattice QCD LQCD quantization 1 QuantumChromoDynamics Continuum QCD Quantization Lattice QCD LQCD quantization 2 Pure gauge theory Monte Carlo integration Confinement at strong coupling How to set the scale? The three limits of LQCD Christian B. Lang Lattice QCD for Pedestrians Continuum QCD QuantumChromoDynamics Quantization Pure gauge theory Lattice QCD LQCD quantization Continuum QCD “Declaration of QCD” We assume that QCD is the quantum field theory of quarks and gluons, defined by a Lagrangian and action of the form 1 L = Tr F F + ψ (D/ + m ) ψ 2 g2 µν µν f f f Xf S = d 4x L Z This theory can be solved from first principles, with minimal number of input parameters (bare quark masses and a scale fixing parameter). Hadron properties should be computable from QCD. Christian B. Lang Lattice QCD for Pedestrians Continuum QCD QuantumChromoDynamics Quantization Pure gauge theory Lattice QCD LQCD quantization Euclidean space-time: xµ real, x4 = i t. Quarks ψf : flavor f = u, d, s, c, t, b; color c = 1, 2, 3 Gluons Aµ: Fµν = ∂µAν − ∂ν Aµ + i [Aµ, Aν ] Parameters (couplings): g, mu, md , ms, mc, mt , mb (note: bare parameters, scale dependence!) Homework Mental gymnastics: Imagine what changes, if SU(3) → U(1) e.g., Photons: Aµ: Fµν = ∂µAν − ∂ν Aµ Christian B.
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