|Source:||Bjoern Medeke, Department of Mathematics, Institute of Applied Computer Science, University of Wuppertal, 42097 Wuppertal, Germany. Phone: +49 202 439-3776. Email: email@example.com|
Background. Lattice gauge theory is a discretization of quantum chromodynamics which is generally accepted to be the fundamental physical theory of strong interactions among the quarks as constituents of matter. The most time-consuming part of a numerical simulation in lattice gauge theory with Wilson fermions on the lattice is the computation of quark propagators within a chromodynamic background gauge field. These computations use up a major part of the world's high performance computing power.
Quark propagators are obtained by solving the inhomogeneous lattice Dirac equation Ax = b, where A = I - kD with 0 <= k < kc is a large but sparse complex non-Hermitian matrix representing a periodic nearest-neighbour coupling on a four-dimensional Euclidean space-time lattice.
From the physical theory it is clear that the matrix A should be positive real (all eigenvalues lie in the right half plane) for 0 <= k < kc. Here, kc represents a critical parameter which depends on the given matrix D. Denoting
Due to the nearest neighbour coupling, the matrix A has 'property A'. This means that with a red-black (or odd-even) ordering of the grid points the matrix becomes
Set of QCD Matrices. The QCD matrices provided in the set QCD consist of realistic matrices D generated at different physical temperatures b.
References. A survey of lattice gauge theory is given in
A PostScript version of this information is also available.
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