mesq.cc

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#error "NOT FULLY CONVERTED"
 
/* Return the value of the trivial geometric definition of */
/* the topological Charge */
 
/* Only for U(1) in 2 dim (Nc=1,Nd=2)*/
 
/* u -- gauge field (Read) */
/* q -- topological charge (Write) */
 
include(types.mh)
 
SUBROUTINE(MesQ, u, q)
 
multi1d<LatticeColorMatrix> u(Nd);
Double q;
{
  include(COMMON_DECLARATIONS)
  
  LatticeColorMatrix tmp_0;
  LatticeColorMatrix tmp_1;
  LatticeComplex wplaq_tmp;
  LatticeReal tmp_r;
  LatticeReal tmp_x;
  LatticeReal tmp_y;
  LatticeReal phi;
 
  Double tmp;
  Double tmp2;
  Double tmp3;
 
  int cb;
  int mu;
  int nu;
 
  START_CODE();
   
               
  phi = 0;
 
  if ( Nd != 2 ) 
    QDP_error_exit("only support 2 dimensions");
 
  if ( Nc != 1 ) 
    QDP_error_exit("only support for U[1]);
  
  mu=0;
  nu=1;
 
  for(cb=0; cb < 2; ++cb)
  {
    /* tmp_0 = u(x+mu,nu)*u_dag(x+nu,mu) */
    tmp_0 = shift(u[nu][1-cb], cb, FORWARD, mu) * shift(adj[u[mu][1-cb]], cb, FORWARD, nu);
    
    /* tmp_1 = tmp_0*u_dag(x,nu)=u(x+mu,nu)*u_dag(x+nu,mu)*u_dag(x,nu) */
    tmp_1 = tmp_0 * adj(u[nu][cb]);
    
    /* wplaq_tmp = tr(u(x,mu)*tmp_1=u(x,mu)*u(x+mu,nu)*u_dag(x+nu,mu)*u_dag(x,nu)) */
    wplaq_tmp = trace(u[mu][cb] * tmp_1);
    
    tmp_x = real(wplaq_tmp);
    tmp_y = imag(wplaq_tmp);
    tmp_r = atan2(tmp_y, tmp_x);
    phi += tmp_r;
  }
 
  tmp = -sum(phi);
 
              
  tmp2 = 8*atan(1);
  q = tmp / tmp2;
 
  END_CODE();
}