su2extract.cc

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/*! \file
 *  \brief  Extract an unnormalized SU(2) matrix from a GL(3,C) matrix
 */
 
#include "chromabase.h"
#include "util/gauge/su2extract.h"
 
namespace Chroma  
{
 
  //! Su2_extract: r_0,r_1,r_2,r_3 <- source(su2_index)  [SU(N) field]  under a subset
  /*! 
   * \ingroup gauge
   *
   * Extract components r_k proportional to SU(2) submatrix su2_index
   * from the "SU(Nc)" matrix V. The SU(2) matrix is parametrized in the
   * sigma matrix basis.
   *
   * There are Nc*(Nc-1)/2 unique SU(2) submatrices in an SU(Nc) matrix.
   * The user does not need to know exactly which one is which, just that
   * they are unique.
   *
   * Arguments:
   *
   * \param r           su(2) matrix represented in the O(4) rep. - an array of LatticeReal 
   * \param source      extract the su2 matrix from this su(n) gauge field
   * \param su2_index   int lying in [0, Nc*(Nc-1)/2)
   * \param s           subset for operations       (Read)
   */
 
  template<typename S>
  inline
  void
  su2Extract_t(multi1d<LatticeReal>& r,
               const LatticeColorMatrix& source, 
               int su2_index, 
               const S& s)
  {
    START_CODE();
 
    if (r.size() != 4)
    {
      QDPIO::cerr << "su2Extract: return result invalid size" << std::endl;
      QDP_abort(1);
    }
 
    /* Determine the SU(N) indices corresponding to the SU(2) indices */
    /* of the SU(2) subgroup $3 */
    int i1, i2;
    int found = 0;
    int del_i = 0;
    int index = -1;
 
    while ( del_i < (Nc-1) && found == 0 )
    {
      del_i++;
      for ( i1 = 0; i1 < (Nc-del_i); i1++ )
      {
        index++;
        if ( index == su2_index )
        {
          found = 1;
          break;
        }
      }
    }
    i2 = i1 + del_i;
 
    if ( found == 0 )
    {
      QDPIO::cerr << __func__ << ": trouble with SU2 subgroup index" << std::endl;
      QDP_abort(1);
    }
 
    /* Compute the b(k) of A_SU(2) = b0 + i sum_k bk sigma_k */ 
    r[0][s] = real(peekColor(source,i1,i1)) + real(peekColor(source,i2,i2));
    r[1][s] = imag(peekColor(source,i1,i2)) + imag(peekColor(source,i2,i1));
    r[2][s] = real(peekColor(source,i1,i2)) - real(peekColor(source,i2,i1));
    r[3][s] = imag(peekColor(source,i1,i1)) - imag(peekColor(source,i2,i2));
 
    END_CODE();
  }
 
 
  void
  su2Extract(multi1d<LatticeReal>& r,
             const LatticeColorMatrix& source, 
             int su2_index, 
             const Subset& s)
  {
    su2Extract_t(r, source, su2_index, s);
  }
 
 
}  // end namespace Chroma