Difference between revisions of "Overlap"
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The overlap operator preserves chiral symmetry on the lattice, and is the most ideal operator used to explore low pion masses. | The overlap operator preserves chiral symmetry on the lattice, and is the most ideal operator used to explore low pion masses. | ||
The massless overlap is defined by | The massless overlap is defined by | ||
| − | <math>D_0 = \rho(1+\gamma_5)\epsilon(H)</math> | + | |
| − | Given a vector <math>\vec{\eta}</math> | + | <math>\mathbf{D_0} = \rho(1+\gamma_5)\varepsilon(H)</math> |
| + | |||
| + | Where <math>\rho= 4 - 1/2\kappa</math>, <math>\kappa </math> is a positive number. | ||
| + | <math>H</math> is the hermitian Wilson operator, and <math>\epsilon(H)</math> is the matrix sign function. | ||
| + | Given a vector <math>\vec{\eta}</math>, we want to compute the solution <math>\vec{x}</math>, which is the matrix vector multiplication | ||
| + | |||
| + | <math>\mathbf{D_0} \vec{\eta} = \vec{x} </math> | ||
Latest revision as of 09:29, 31 August 2010
The intention of these notes is to outline how we construct the overlap operator in the gwu-qcd framework. The overlap operator preserves chiral symmetry on the lattice, and is the most ideal operator used to explore low pion masses. The massless overlap is defined by
\(\mathbf{D_0} = \rho(1+\gamma_5)\varepsilon(H)\)
Where \(\rho= 4 - 1/2\kappa\), \(\kappa \) is a positive number. \(H\) is the hermitian Wilson operator, and \(\epsilon(H)\) is the matrix sign function. Given a vector \(\vec{\eta}\), we want to compute the solution \(\vec{x}\), which is the matrix vector multiplication
\(\mathbf{D_0} \vec{\eta} = \vec{x} \)
