barspinmat_w.cc

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/*! \file
 *  \brief Baryon spin and projector matrices
 */
 
#include "chromabase.h"
#include "meas/hadron/barspinmat_w.h"
 
namespace Chroma 
{
 
  /*! \ingroup hadron */
  namespace BaryonSpinMats
  {
    //! NR = (1/2)* ( 1 + g_4 )
    SpinMatrix NR()
    {
      SpinMatrix g_one = 1.0;
      return SpinMatrix(0.5 * (g_one + (g_one * Gamma(8))));
    }
 
    //! NRnegPar = (1/2)* ( 1 - g_4 )
    SpinMatrix NRnegPar()
    {
      SpinMatrix g_one = 1.0;
      return SpinMatrix(0.5 * (g_one - (g_one * Gamma(8))));
    }
 
    //! C = Gamma(10)
    SpinMatrix C()
    {
      return SpinMatrix(Gamma(10) * SpinMatrix(1.0));
    }
 
    //! C NR = (1/2)*C * ( 1 + g_4 )
    SpinMatrix CNR()
    {
      SpinMatrix g_one = 1.0;
      return SpinMatrix(Gamma(10) * NR());
    }
 
    //! C gamma_5 gamma_4 = - Gamma(13)
    SpinMatrix Cg5g4()
    {
      SpinMatrix g_mone = -1.0;
      return SpinMatrix(Gamma(13) * g_mone);
    }
 
    //! C g_k = C gamma_k
    SpinMatrix Cgk(int k)
    {
      SpinMatrix g_one = 1.0;
      SpinMatrix gt;
 
      // NOTE: not being too careful about minus signs. Should check.
      // However, all current uses have these matrices coming as a square
      switch (k)
      {
      case 1:
        gt = Gamma(11) * g_one;
        break;
 
      case 2:
        gt = Gamma(8) * g_one;
        break;
 
      case 3:
        gt = Gamma(14) * g_one;
        break;
 
      default:
        gt = g_one;  // Make compiler happy
        QDPIO::cerr << __func__ << ": invalid k=" << k << std::endl;
        QDP_abort(1);
      }
      return gt;
    }
 
    //! C g_\mu = \gamma_4 \gamma_2 \gamma_\mu
    SpinMatrix Cgmu(int k)
    {
      SpinMatrix g_one = 1.0;
      SpinMatrix gt;
 
      //signs have been checked...
      switch (k)
      {
      case 1:
        gt = Gamma(11) * g_one;
        break;
 
      case 2:
        gt = -(Gamma(8) * g_one);
        break;
 
      case 3:
        gt = -(Gamma(14) * g_one);
        break;
 
      case 4:
        gt = Gamma(2) * g_one;
        break;
 
      default:
        gt = g_one;  // Make compiler happy
        QDPIO::cerr << __func__ << ": invalid k=" << k << std::endl;
        QDP_abort(1);
      }
      return gt;
    }
 
    //! C g_\mu = \gamma_4 \gamma_2 transpose(\gamma_\mu)
    SpinMatrix CgmuTrans(int k)
    {
      k--; //for compatibility with the Cgmu
      SpinMatrix g_one = 1.0;
      SpinMatrix gt;
      //QDPIO::cout<<"CgmuTrans("<<k<<")"<<std::endl ;
      SpinMatrix gmu = Gamma(1<<k)*g_one ;
      
      //signs have been checked...
      // Gamma(10) = gamma_2 gamma_4
      gt = Gamma(10)*transpose(gmu);
 
      return gt;
    }
 
    //! C g4 g_k = C gamma_4 gamma_k
    SpinMatrix Cg4gk(int k)
    {
      SpinMatrix g_one = 1.0;
      SpinMatrix gt;
 
      // NOTE: not being too careful about minus signs. Should check.
      // However, all current uses have these matrices coming as a square
      switch (k)
      {
      case 1:
        gt = Gamma(3) * g_one;
        break;
 
      case 2:
        gt = Gamma(0) * g_one;
        break;
 
      case 3:
        gt = Gamma(6) * g_one;
        break;
 
      default:
        gt = g_one;  // Make compiler happy
        QDPIO::cerr << __func__ << ": invalid k=" << k << std::endl;
        QDP_abort(1);
      }
      return gt;
    }
 
    //! C g_k NR = C gamma_k (1/2)(1 + gamma_4)
    SpinMatrix CgkNR(int k)
    {
      return SpinMatrix(Cgk(k) * NR());
    }
 
 
    //! C g_5 = C gamma_5 = Gamma(5)
    SpinMatrix Cg5()
    {
      return SpinMatrix(Gamma(5) * SpinMatrix(1.0));
    }
 
 
    //! C g_5 NR = (1/2)*C gamma_5 * ( 1 + g_4 )
    SpinMatrix Cg5NR()
    {
      return SpinMatrix(Gamma(5) * NR());
    }
 
    //! C g_5 NR = (1/2)*C gamma_5 * ( 1 - g_4 )
    SpinMatrix Cg5NRnegPar()
    {
      SpinMatrix g_one = 1.0;
 
      return SpinMatrix(Gamma(5) * NRnegPar());
    }
 
    //! C gamma_- = Cgm = (C gamma_-)^T
    SpinMatrix Cgm()
    {
      SpinMatrix g_one = 1.0;
      SpinMatrix g_tmp1 = 0.5 * (Gamma(2) * g_one  +  timesI(Gamma(1) * g_one));
      return SpinMatrix(Gamma(10) * g_tmp1);
    }
 
    //! C gamma_4 gamma_- = Cg4m
    SpinMatrix Cg4m()
    {
      SpinMatrix g_one = 1.0;
      SpinMatrix g_tmp1 = 0.5 * (Gamma(2) * g_one  +  timesI(Gamma(1) * g_one));
      return SpinMatrix(Gamma(10) * (Gamma(8) * g_tmp1));
    }
 
    //! C gamma_- NR = CgmNR = C gamma_- (1/2)(1 + gamma_4)
    SpinMatrix CgmNR()
    {
      return SpinMatrix(Cgm() * NR());
    }
 
    //! C gamma_+ = Cgm = (C gamma_+)^T
    SpinMatrix Cgp()
    {
      SpinMatrix g_one = 1.0;
      SpinMatrix g_tmp1 = 0.5 * (timesI(Gamma(1) * g_one) - Gamma(2) * g_one);
      return SpinMatrix(Gamma(10) * g_tmp1);
    }
 
    //! C gamma_4 gamma_+ = Cg4p
    SpinMatrix Cg4p()
    {
      SpinMatrix g_one = 1.0;
      SpinMatrix g_tmp1 = 0.5 * (timesI(Gamma(1) * g_one) - Gamma(2) * g_one );
      return SpinMatrix(Gamma(10) * (Gamma(8) * g_tmp1));
    }
 
    //! C gamma_+ NR = CgpNR = C gamma_+ (1/2)(1 + gamma_4)
    SpinMatrix CgpNR()
    {
      return SpinMatrix(Cgp() * NR());
    }
 
 
 
 
    //! T = (1 + gamma_4) / 2 = (1 + Gamma(8)) / 2
    SpinMatrix Tunpol()
    {
      return NR();
    }
 
 
    //! T = (1 + gamma_4) / 2 = (1 - Gamma(8)) / 2
    SpinMatrix TunpolNegPar()
    {
      return NRnegPar();
    }
 
 
    //! T = \Sigma_3 (1 + gamma_4) / 2 = -i (Gamma(3) + Gamma(11)) / 2
    SpinMatrix Tpol()
    {
      SpinMatrix g_one = 1.0;
      return SpinMatrix(0.5 * timesMinusI(Gamma(3)*g_one + Gamma(11)*g_one));
    }
 
    //! T = \Sigma_3 (1 - gamma_4) / 2 = -i (-Gamma(3) + Gamma(11)) / 2
    SpinMatrix TpolNegPar()
    {
      SpinMatrix g_one = 1.0;
      return SpinMatrix(0.5 * timesMinusI(Gamma(11)*g_one-Gamma(3)*g_one));
    }
 
 
    //! T = (1 + \Sigma_3)*(1 + gamma_4) / 2   = (1 + Gamma(8) - i G(3) - i G(11)) / 2
    SpinMatrix Tmixed()
    {
      SpinMatrix g_one = 1.0;
      return SpinMatrix(0.5*(g_one + Gamma(8)*g_one + timesMinusI(Gamma(3)*g_one + Gamma(11)*g_one)));
    }
 
    //! T = (1 - \Sigma_3)*(1 - gamma_4) / 2   = (1 - Gamma(8) + i G(3) - i G(11)) / 2
    // Need to flip the spin for time reversal
    SpinMatrix TmixedNegPar()
    {
      SpinMatrix g_one = 1.0;
      return SpinMatrix(0.5*(g_one - Gamma(8)*g_one + timesMinusI(Gamma(3)*g_one - Gamma(11)*g_one)));
    }
 
    //! T = (1 + i \gamma_5 \gamma_3 )/2 = 1/2 *( 1  - iG(11) )
    SpinMatrix TspinUp(){
      SpinMatrix g_one = 1.0;
      return SpinMatrix(0.5*(g_one + timesMinusI(Gamma(11)*g_one)));
    }
    //! T = (1 - i \gamma_5 \gamma_3 )/2 = 1/2 *( 1  + iG(11) )
    SpinMatrix TspinDown(){
      SpinMatrix g_one = 1.0;
      return SpinMatrix(0.5*(g_one - timesMinusI(Gamma(11)*g_one)));
    }
 
#ifndef _FRANKLIN_
    //! T = i \gamma_5 (\gamma_1 + i \gamma_2 )
    SpinMatrix T_ig5XpiY(){
      SpinMatrix g_one = 1.0;
      SpinMatrix tt = (Gamma(1)*g_one - timesMinusI(Gamma(2)*g_one));
      return SpinMatrix(-timesMinusI(Gamma(15)*tt));
    }
    //! T = i \gamma_5 (\gamma_1 - i \gamma_2 )
    SpinMatrix T_ig5XmiY(){
      SpinMatrix g_one = 1.0;
      SpinMatrix tt = (Gamma(1)*g_one + timesMinusI(Gamma(2)*g_one));
      return SpinMatrix(-timesMinusI(Gamma(15)*tt));
    }
#else
    //FIX FRANKLIN GNU COMPILER BUG
    //! T = i \gamma_5 (\gamma_1 - i \gamma_2 )
    SpinMatrix T_ig5XmiY( )
    {
      SpinMatrix g_one = 1.0;
      //SpinMatrix tt = (Gamma(1)*g_one + timesMinusI(Gamma(2)*g_one));
      SpinMatrix tt = (Gamma(14)*g_one - timesMinusI(Gamma(13)*g_one));
      return SpinMatrix(timesMinusI(tt));
    }
 
    //! T = i \gamma_5 (\gamma_1 + i \gamma_2 )
    SpinMatrix T_ig5XpiY(){
      SpinMatrix g_one = 1.0;
      SpinMatrix tt = (Gamma(14)*g_one + timesMinusI(Gamma(13)*g_one));
      return SpinMatrix(timesMinusI(tt));
    }
#endif
    
  }
 
} // end namespace