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Gauge Fixing in Lattice QCD on GPUs

Mario Schrock
WS 10/11 Report, 2011

@article{schrock2011gauge,

   title={Gauge Fixing in Lattice QCD on GPUs},

   author={Schrock, Mario},

   year={2011}

}

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Quantum Chromodynamics (QCD) [1, 2] is the theory of the strong interaction which is responsible for the hadron spectrum and therefore for all matter in our everyday life. QCD, being a quantum field theory and part of the standard model of elementary particles, describes the interactions between color-charged quarks and gluons. Hadrons, e.g., protons, neutrons and the pion, to name the most famous, are made up of two or three quarks, respectively, "glued" together by gluons to build a color-neutral particle. In 1974, Wilson [3] proposed a formulation of gauge theories such as QCD on a discrete four dimensional space-time lattice. This work concentrates on the gluonic part of QCD which is described by a real valued vector field A_mu(x), mu = 1, …, 4. When switching from the continuum to the discrete formulation on a space-time lattice, the gauge field A_mu(x) gets replaced by the group valued field U_mu(x) in SU(3) which is connected to its continuum version via U_mu(x) = exp(iaA_mu(x)) where a is the lattice spacing. The field variables U_mu(x) are said to live between neighboring lattice sites x and x + mu and thus are commonly referred to as link variables.
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