mesfield.cc

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/*! \file
 *  \brief Calculates the antihermitian field strength tensor  iF(mu,nu)
 */
 
#include "chromabase.h"
#include "meas/glue/mesfield.h"
 
namespace Chroma 
{
 
  //! Calculates the antihermitian field strength tensor  iF(mu,nu)
  /*
   * \ingroup glue
   *
   *    F(mu,nu) =  (1/4) sum_p (1/2) [ U_p(x) - U^dag_p(x) ]
   *
   *  where
   *    U_1 = u(x,mu)*u(x+mu,nu)*u_dag(x+nu,mu)*u_dag(x,nu)
   *    U_2 = u(x,nu)*u_dag(x-mu+nu,mu)*u_dag(x-mu,nu)*u(x-mu,mu)
   *    U_3 = u_dag(x-mu,mu)*u_dag(x-mu-nu,nu)*u(x-mu-nu,mu)*u(x-nu,nu)
   *    U_4 = u_dag(x-nu,nu)*u(x-nu,mu)*u(x-nu+mu,nu)*u_dag(x,mu)
 
   *  NOTE: I am using  i*F  of the usual F defined by UKQCD, Heatlie et.al.
 
   * Arguments:
 
   *  \param f   field strength tensor f(mu,nu) (Write)
   *  \param u   gauge field (Read)
   */
  template<typename U>
  void mesFieldT(multi1d<U>& f,
                const multi1d<U>& u)
  {
    START_CODE();
 
    f.resize(Nd*(Nd-1)/2);
    
    U tmp_0;
    U tmp_1;
    U tmp_2;
    U tmp_3;
    U tmp_4;
 
    Real fact = 0.125;
  
    int offset = 0;
 
    for(int mu=0; mu < Nd-1; ++mu)
    {
      for(int nu=mu+1; nu < Nd; ++nu)
      {
        tmp_3 = shift(u[nu], FORWARD, mu);
        tmp_4 = shift(u[mu], FORWARD, nu);
        tmp_0 = u[nu] * tmp_4;
        tmp_1 = u[mu] * tmp_3;
 
        f[offset] = tmp_1 * adj(tmp_0);
 
        tmp_2 = adj(tmp_0) * tmp_1;
        tmp_1 = shift(tmp_2, BACKWARD, nu);
        f[offset] += shift(tmp_1, BACKWARD, mu);
        tmp_1 = tmp_4 * adj(tmp_3);
        tmp_0 = adj(u[nu]) * u[mu];
 
        f[offset] += shift(tmp_0*adj(tmp_1), BACKWARD, nu);
        f[offset] += shift(adj(tmp_1)*tmp_0, BACKWARD, mu);
 
        tmp_0 = adj(f[offset]);
        f[offset] -= tmp_0;
        f[offset] *= fact;
 
        ++offset;
      }
    }
  
            
    END_CODE();
  }
 
  void mesField(multi1d<LatticeColorMatrixF>& f,
                const multi1d<LatticeColorMatrixF>& u) 
  {
    mesFieldT(f,u);
  }
 
  void mesField(multi1d<LatticeColorMatrixD>& f,
                const multi1d<LatticeColorMatrixD>& u) 
  {
    mesFieldT(f,u);
  }
 
 
}  // namespace Chroma