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104 lines
3.6 KiB
C++
104 lines
3.6 KiB
C++
/*
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* Policy classes for the HMC
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* Authors: Guido Cossu, David Preti
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*/
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#ifndef SUN2INDEX_H_H
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#define SUN2INDEX_H_H
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NAMESPACE_BEGIN(Grid);
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/*
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* This is an helper class for the HMC
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* Should contain only the data for the two index representations
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* and the facility to convert from the fundamental -> two index
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* The templated parameter TwoIndexSymmetry choses between the
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* symmetric and antisymmetric representations
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*
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* There is an
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* enum TwoIndexSymmetry { Symmetric = 1, AntiSymmetric = -1 };
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* in the SUnTwoIndex.h file
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*/
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template <int ncolour, TwoIndexSymmetry S, class group_name = GroupName::SU>
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class TwoIndexRep {
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public:
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// typdef to be used by the Representations class in HMC to get the
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// types for the higher representation fields
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typedef typename GaugeGroupTwoIndex<ncolour, S, group_name>::LatticeTwoIndexMatrix LatticeMatrix;
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typedef typename GaugeGroupTwoIndex<ncolour, S, group_name>::LatticeTwoIndexField LatticeField;
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static const int Dimension = GaugeGroupTwoIndex<ncolour,S,group_name>::Dimension;
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static const bool isFundamental = false;
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LatticeField U;
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explicit TwoIndexRep(GridBase *grid) : U(grid) {}
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void update_representation(const LatticeGaugeField &Uin) {
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std::cout << GridLogDebug << "Updating TwoIndex representation\n";
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// Uin is in the fundamental representation
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// get the U in TwoIndexRep
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// (U)_{(ij)(lk)} = tr [ adj(e^(ij)) U e^(lk) transpose(U) ]
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conformable(U, Uin);
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U = Zero();
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LatticeColourMatrix tmp(Uin.Grid());
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Vector<typename GaugeGroup<ncolour,group_name>::Matrix> eij(Dimension);
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for (int a = 0; a < Dimension; a++)
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GaugeGroupTwoIndex<ncolour, S, group_name>::base(a, eij[a]);
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for (int mu = 0; mu < Nd; mu++) {
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auto Uin_mu = peekLorentz(Uin, mu);
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auto U_mu = peekLorentz(U, mu);
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for (int a = 0; a < Dimension; a++) {
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tmp = transpose(Uin_mu) * adj(eij[a]) * Uin_mu;
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for (int b = 0; b < Dimension; b++)
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pokeColour(U_mu, trace(tmp * eij[b]), a, b);
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}
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pokeLorentz(U, U_mu, mu);
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}
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}
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LatticeGaugeField RtoFundamentalProject(const LatticeField &in,
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Real scale = 1.0) const {
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LatticeGaugeField out(in.Grid());
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out = Zero();
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for (int mu = 0; mu < Nd; mu++) {
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LatticeColourMatrix out_mu(in.Grid()); // fundamental representation
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LatticeMatrix in_mu = peekLorentz(in, mu);
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out_mu = Zero();
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typename GaugeGroup<ncolour, group_name>::LatticeAlgebraVector h(in.Grid());
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projectOnAlgebra(h, in_mu, double(Nc + 2 * S)); // factor T(r)/T(fund)
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FundamentalLieAlgebraMatrix(h, out_mu); // apply scale only once
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pokeLorentz(out, out_mu, mu);
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}
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return out;
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}
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private:
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void projectOnAlgebra(typename GaugeGroup<ncolour, group_name>::LatticeAlgebraVector &h_out,
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const LatticeMatrix &in, Real scale = 1.0) const {
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GaugeGroupTwoIndex<ncolour, S,group_name>::projectOnAlgebra(h_out, in, scale);
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}
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void FundamentalLieAlgebraMatrix(
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typename GaugeGroup<ncolour, group_name>::LatticeAlgebraVector &h,
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typename GaugeGroup<ncolour, group_name>::LatticeMatrix &out, Real scale = 1.0) const {
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GaugeGroup<ncolour,group_name>::FundamentalLieAlgebraMatrix(h, out, scale);
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}
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};
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typedef TwoIndexRep<Nc, Symmetric, GroupName::SU> TwoIndexSymmetricRepresentation;
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typedef TwoIndexRep<Nc, AntiSymmetric, GroupName::SU> TwoIndexAntiSymmetricRepresentation;
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typedef TwoIndexRep<Nc, Symmetric, GroupName::Sp> SpTwoIndexSymmetricRepresentation;
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typedef TwoIndexRep<Nc, AntiSymmetric, GroupName::Sp> SpTwoIndexAntiSymmetricRepresentation;
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NAMESPACE_END(Grid);
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#endif
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