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documentation for gaugegroup and sp2n

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Alessandro Lupo 2023-05-25 18:40:54 +01:00
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@ -2778,47 +2778,83 @@ and there are associated reconstruction routines for assembling four spinors fro
These ca
SU(N)
Gauge Group
--------
A generic Nc qcd/utils/GaugeGroup.h is provided. This defines a template class that can be specialised to different gauge groups::
A generic Nc qcd/utils/SUn.h is provided. This defines a template class::
template <int ncolour, class group_name>
class GaugeGroup {...}
template <int ncolour> class SU ;
Supported groups are SU(N) and Sp(2N). The group can be specified through the GroupName namespace::
The most important external methods are::
namespace GroupName {
class SU {};
class Sp {};
}
A simpler interface is achieved by instantiating the GaugeGroup class with a specific group::
template <int ncolour>
using SU = GaugeGroup<ncolour, GroupName::SU>;
template <int ncolour>
using Sp = GaugeGroup<ncolour, GroupName::Sp>;
Specific instantiations are then defined::
typedef SU<2> SU2;
typedef SU<3> SU3;
typedef SU<4> SU4;
typedef SU<5> SU5;
typedef Sp<2> Sp2;
typedef Sp<4> Sp4;
typedef Sp<6> Sp6;
typedef Sp<8> Sp8;
Some methods are common to both gauge groups. The most important common external methods are::
static void printGenerators(void) ;
template <class cplx> static void generator(int lieIndex, iSUnMatrix<cplx> &ta) ;
static void GaussianFundamentalLieAlgebraMatrix(GridParallelRNG &pRNG,
LatticeMatrix &out,
Real scale = 1.0) ;
static void HotConfiguration(GridParallelRNG &pRNG, GaugeField &out) ;
static void TepidConfiguration(GridParallelRNG &pRNG,GaugeField &out);
static void ColdConfiguration(GaugeField &out);
static void taProj( const LatticeMatrixType &in, LatticeMatrixType &out);
static void taExp(const LatticeMatrixType &x, LatticeMatrixType &ex) ;
Whenever needed, a different implementation of these methods for the gauge groups is achieved by overloading. For example,::
template <typename LatticeMatrixType> // shared interface for the traceless-antihermitian projection
static void taProj(const LatticeMatrixType &in, LatticeMatrixType &out) {
taProj(in, out, group_name());
}
template <typename LatticeMatrixType> // overloaded function to SU(N) simply perform Ta
static void taProj(const LatticeMatrixType &in, LatticeMatrixType &out, GroupName::SU) {
out = Ta(in);
}
template <typename LatticeMatrixType> // overloaded function to Sp(2N) must use a modified Ta function
static void taProj(const LatticeMatrixType &in, LatticeMatrixType &out, GroupName::Sp) {
out = SpTa(in);
}
Gauge Group: SU(N)
--------
The specialisation of GaugeGroup to SU(N), formally part of qcd/utils/GaugeGroup.h, is found in the file qcd/utils/SUn.impl
It contains methods that are only implemented for SU(N), and specialisations of shared methods to the special unitary group
The most important external methods are::
static void SubGroupHeatBath(GridSerialRNG &sRNG, GridParallelRNG &pRNG, RealD beta, // coeff multiplying staple in action (with no 1/Nc)
LatticeMatrix &link,
const LatticeMatrix &barestaple, // multiplied by action coeffs so th
int su2_subgroup, int nheatbath, LatticeInteger &wheremask);
static void GaussianFundamentalLieAlgebraMatrix(GridParallelRNG &pRNG,
LatticeMatrix &out,
Real scale = 1.0) ;
static void GaugeTransform( GaugeField &Umu, GaugeMat &g)
static void RandomGaugeTransform(GridParallelRNG &pRNG, GaugeField &Umu, GaugeMat &g);
static void HotConfiguration(GridParallelRNG &pRNG, GaugeField &out) ;
static void TepidConfiguration(GridParallelRNG &pRNG,GaugeField &out);
static void ColdConfiguration(GaugeField &out);
static void taProj( const LatticeMatrixType &in, LatticeMatrixType &out);
static void taExp(const LatticeMatrixType &x, LatticeMatrixType &ex) ;
static int su2subgroups(void) ; // returns how many subgroups
Specific instantiations are defined::
typedef SU<2> SU2;
typedef SU<3> SU3;
typedef SU<4> SU4;
typedef SU<5> SU5;
For example, Quenched QCD updating may be run as (tests/core/Test_quenched_update.cc)::
for(int sweep=0;sweep<1000;sweep++){
@ -2857,6 +2893,16 @@ For example, Quenched QCD updating may be run as (tests/core/Test_quenched_updat
}
}
Gauge Group: Sp(2N)
--------
The specialisation of GaugeGroup to Sp(2N), formally part of qcd/utils/GaugeGroup.h, is found in the file qcd/utils/Sp(2N).impl
It contains methods that are only implemented for Sp(2N), and specialisations of shared methods to the special unitary group
The most important external methods are::
static void Omega(LatticeColourMatrixD &in) // Symplectic matrix left invariant by Sp(2N)
Generation of Sp(2N) gauge fields is only supported via HMC.
Space time grids
----------------