Exercise 7: Rho Meson
Goals: Computing vector meson two-point function
Concepts: Gamma matrices
Directory: $HOME/examples/07-rho
How to: $ cd $HOME/examples/07-rho
$ make
$ submit rho /scratch/data/beta6_gauge_8x8x8x16 0.1493

In this exercise we compute a vector meson two point function and introduce γ matrices. QDP has a hardwired prepresentation of the Clifford algebra basis that is used by all routines in the library. The user can access the γ-matrices by using a small integer. All products of γ-matrices can be expresses as a product of the following form: γ1aγ2bγ3cγ4d where each of a, b, c and d is either 0 or 1. Then the index of this particular product is the number [dcba]2. Since Sρ = Trt(Pγ1PTγ1), and P=γ5P+γ5, one computes Sρ as follows (this is rho.c). Since γ-matrices do not commute, we need to be mindful on which side of the propagator they are, see lines 37 and 38) 

 12   print_rho(QDP_DiracPropagator *prop, int t0)
 13   {
 14     int i, nt, gamma;
 15     QLA_Complex *corr;
 16     QDP_DiracPropagator *prop_gamma, *gamma_prop_gamma;
...
 29     /* allocate temporary propagators */
 30     prop_gamma = QDP_create_P();
 31     gamma_prop_gamma = QDP_create_P();
 32
 33     /* gamma_1 gamma_5 = g_2 g_3 g_4 -> 1110_2 = 15 - 1 */
 34     gamma = 15 - 1;
 35
 36     /* multiply prop by GAMMA on both sides */
 37     QDP_P_eq_P_times_gamma(prop_gamma, prop, gamma, QDP_all);
 38     QDP_P_eq_gamma_times_P(gamma_prop_gamma, prop_gamma, gamma, QDP_all);
 39
 40     /* do sum[trace(prop^+ GAMMA prop GAMMA)] over each timeslice */
 41     QDP_c_eq_P_dot_P_multi(corr, prop, gamma_prop_gamma, timeslices, nt);
The propagator now is complex. We print only the real part of it: 
 43     /* print result */
 44     printf0("BEGIN RHO\n");
 45     for(i=0; i<nt; i++) {
 46       int t = (t0+i)%nt;
 47       printf0("%i\t%g\n", i, -QLA_real(corr[t]) );
 48     }
 49     printf0("END RHO\n");

Problems