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115 lines
3.4 KiB
C++
115 lines
3.4 KiB
C++
/*
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* Policy classes for the HMC
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* Author: Guido Cossu
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*/
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#ifndef ADJOINT_H
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#define ADJOINT_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 adjoint representation
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* and the facility to convert from the fundamental -> adjoint
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*/
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template <int ncolour>
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class AdjointRep {
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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 SU_Adjoint<ncolour>::LatticeAdjMatrix LatticeMatrix;
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typedef typename SU_Adjoint<ncolour>::LatticeAdjField LatticeField;
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static const int Dimension = ncolour * ncolour - 1;
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LatticeField U;
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explicit AdjointRep(GridBase *grid) : U(grid) {}
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void update_representation(const LatticeGaugeField &Uin) {
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std::cout << GridLogDebug << "Updating adjoint representation\n";
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// Uin is in the fundamental representation
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// get the U in AdjointRep
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// (U_adj)_B = tr[e^a U e^b U^dag]
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// e^a = t^a/sqrt(T_F)
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// where t^a is the generator in the fundamental
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// T_F is 1/2 for the fundamental representation
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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 SU<ncolour>::Matrix> ta(Dimension);
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// Debug lines
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// LatticeMatrix uno(Uin._grid);
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// uno = 1.0;
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////////////////
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// FIXME probably not very efficient to get all the generators
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// everytime
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for (int a = 0; a < Dimension; a++) SU<ncolour>::generator(a, ta[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 = 2.0 * adj(Uin_mu) * ta[a] * Uin_mu;
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for (int b = 0; b < Dimension; b++)
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pokeColour(U_mu, trace(tmp * ta[b]), a, b);
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}
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pokeLorentz(U, U_mu, mu);
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// Check matrix U_mu, must be real orthogonal
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// reality
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/*
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LatticeMatrix Ucheck = U_mu - conjugate(U_mu);
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std::cout << GridLogMessage << "Reality check: " << norm2(Ucheck) <<
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std::endl;
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Ucheck = U_mu * adj(U_mu) - uno;
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std::cout << GridLogMessage << "orthogonality check: " << norm2(Ucheck) <<
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std::endl;
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*/
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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 SU<ncolour>::LatticeAlgebraVector h(in._grid);
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projectOnAlgebra(h, in_mu, double(Nc) * 2.0); // factor C(r)/C(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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// Returns traceless antihermitian matrix Nc * Nc.
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// Confirmed
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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 SU<ncolour>::LatticeAlgebraVector &h_out,
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const LatticeMatrix &in, Real scale = 1.0) const {
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SU_Adjoint<ncolour>::projectOnAlgebra(h_out, in, scale);
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}
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void FundamentalLieAlgebraMatrix(
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typename SU<ncolour>::LatticeAlgebraVector &h,
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typename SU<ncolour>::LatticeMatrix &out, Real scale = 1.0) const {
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SU<ncolour>::FundamentalLieAlgebraMatrix(h, out, scale);
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}
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};
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typedef AdjointRep<Nc> AdjointRepresentation;
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NAMESPACE_END(Grid);
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#endif
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