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135 lines
3.9 KiB
C++
135 lines
3.9 KiB
C++
#ifndef QCD_UTILS_WILSON_LOOPS_H
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#define QCD_UTILS_WILSON_LOOPS_H
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namespace Grid {
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namespace QCD {
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// Common wilson loop observables
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template<class GaugeMat,class GaugeLorentz>
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class WilsonLoops {
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public:
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//////////////////////////////////////////////////
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// directed plaquette oriented in mu,nu plane
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//////////////////////////////////////////////////
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static void dirPlaquette(GaugeMat &plaq,const std::vector<GaugeMat> &U, const int mu, const int nu)
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{
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plaq=CovShiftForward(U[mu],mu,U[nu])*adj(CovShiftForward(U[nu],nu,U[mu]));
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}
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//////////////////////////////////////////////////
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// trace of directed plaquette oriented in mu,nu plane
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//////////////////////////////////////////////////
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static void traceDirPlaquette(LatticeComplex &plaq, const std::vector<GaugeMat> &U, const int mu, const int nu)
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{
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GaugeMat sp(U[0]._grid);
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dirPlaquette(sp,U,mu,nu);
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plaq=trace(sp);
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}
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//////////////////////////////////////////////////
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// sum over all planes of plaquette
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//////////////////////////////////////////////////
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static void sitePlaquette(LatticeComplex &Plaq,const std::vector<GaugeMat> &U)
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{
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LatticeComplex sitePlaq(U[0]._grid);
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for(int mu=1;mu<Nd;mu++){
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for(int nu=0;nu<mu;nu++){
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traceDirPlaquette(sitePlaq,U,mu,nu);
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Plaq = Plaq + sitePlaq;
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}
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}
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}
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//////////////////////////////////////////////////
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// sum over all x,y,z,t and over all planes of plaquette
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//////////////////////////////////////////////////
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static RealD sumPlaquette(const GaugeLorentz &Umu){
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std::vector<GaugeMat> U(4,Umu._grid);
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for(int mu=0;mu<Nd;mu++){
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U[mu] = peekIndex<LorentzIndex>(Umu,mu);
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}
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LatticeComplex Plaq(Umu._grid);
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sitePlaquette(Plaq,U);
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TComplex Tp = sum(Plaq);
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Complex p = TensorRemove(Tp);
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return p.real();
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}
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//////////////////////////////////////////////////
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// average over all x,y,z,t and over all planes of plaquette
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//////////////////////////////////////////////////
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static RealD avgPlaquette(const GaugeLorentz &Umu){
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RealD sumplaq = sumPlaquette(Umu);
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double vol = Umu._grid->gSites();
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double faces = (1.0*Nd*(Nd-1))/2.0;
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return sumplaq/vol/faces/Nc; // Nd , Nc dependent... FIXME
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}
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//////////////////////////////////////////////////
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// the sum over all staples on each site
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//////////////////////////////////////////////////
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static void Staple(GaugeMat &staple,GaugeLorentz &Umu,int mu){
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std::vector<GaugeMat> U(4,Umu._grid);
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for(int d=0;d<Nd;d++){
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U[d] = peekIndex<LorentzIndex>(Umu,d);
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}
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staple = zero;
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GaugeMat tmp(U[0]._grid);
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for(int nu=0;nu<Nd;nu++){
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if(nu != mu) {
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// mu
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// ^
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// |__ nu
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// __ __
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// | |
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// __| = __| *
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//
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staple += CovShiftForward(U[nu],nu,U[mu])*Cshift(adj(U[nu]),mu,+1);
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//
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// __ __
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// | |
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// |__ = | * __
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//
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//
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tmp = CovShiftForward (U[mu],mu,U[nu]);
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staple+= CovShiftBackward(U[nu],nu,tmp);
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}
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}
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}
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//////////////////////////////////////////////////////
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// Similar to above for rectangle is required
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//////////////////////////////////////////////////////
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/*
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void siteRectangle(GaugeMat &plaq,const std::vector<GaugeMat> &U, const int mu, const int nu){
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RealD avgRectangle(const std::vector<GaugeMat> &U){}
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RealD avgRectangle(const std::vector<GaugeMat> &U, const int mu, const int nu){}
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void traceRectangle(LatticeComplex &plaq,const std::vector<GaugeMat> &U, const int mu, const int nu){}
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void siteRectangle(GaugeMat &plaq,const std::vector<GaugeMat> &U, const int mu, const int nu){}
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*/
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};
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typedef WilsonLoops<LatticeColourMatrix,LatticeGaugeField> ColourWilsonLoops;
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}}
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#endif
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