- dirac_trace() handles arbitrary expressions (even unexpanded), including

[ginac.git] / ginac / clifford.cpp

diff --git a/ginac/clifford.cpp b/ginac/clifford.cpp
index eb1629d4957aad08f5a001ac2348dc89752a07bb..8a8bfe09294e942e88023d0770784f09d5d9f289 100644 (file)
--- a/ginac/clifford.cpp
+++ b/ginac/clifford.cpp
@@ -24,6 +24,7 @@
 #include "ex.h"
 #include "idx.h"
 #include "ncmul.h"
+#include "symbol.h"
 #include "print.h"
 #include "archive.h"
 #include "debugmsg.h"
@@ -301,7 +302,20 @@ ex dirac_gamma5(unsigned char rl)
        return clifford(diracgamma5(), rl);
 }
 
-ex dirac_trace(const ex & e, unsigned char rl = 0)
+ex dirac_slash(const ex & e, const ex & dim, unsigned char rl)
+{
+       varidx mu((new symbol)->setflag(status_flags::dynallocated), dim);
+       return indexed(e, mu.toggle_variance()) * dirac_gamma(mu, rl);
+}
+
+/** Check whether a given tinfo key (as returned by return_type_tinfo()
+ *  is that of a clifford object with the specified representation label. */
+static bool is_clifford_tinfo(unsigned ti, unsigned char rl)
+{
+       return ti == (TINFO_clifford + rl);
+}
+
+ex dirac_trace(const ex & e, unsigned char rl)
 {
        if (is_ex_of_type(e, clifford)) {
 
@@ -325,12 +339,8 @@ ex dirac_trace(const ex & e, unsigned char rl = 0)
                ex prod = _ex1();
                for (unsigned i=0; i<e.nops(); i++) {
                        const ex &o = e.op(i);
-                       if (is_ex_of_type(o, clifford)
-                        && ex_to_clifford(o).get_representation_label() == rl)
-                               prod *= dirac_trace(o, rl);
-                       else if (is_ex_of_type(o, ncmul)
-                        && is_ex_of_type(o.op(0), clifford)
-                        && ex_to_clifford(o.op(0)).get_representation_label() == rl)
+                       unsigned ti = o.return_type_tinfo();
+                       if (is_clifford_tinfo(o.return_type_tinfo(), rl))
                                prod *= dirac_trace(o, rl);
                        else
                                prod *= o;
@@ -339,10 +349,14 @@ ex dirac_trace(const ex & e, unsigned char rl = 0)
 
        } else if (is_ex_exactly_of_type(e, ncmul)) {
 
-               if (!is_ex_of_type(e.op(0), clifford)
-                || ex_to_clifford(e.op(0)).get_representation_label() != rl)
+               if (!is_clifford_tinfo(e.return_type_tinfo(), rl))
                        return _ex0();
 
+               // Expand product, if necessary
+               ex e_expanded = e.expand();
+               if (!is_ex_of_type(e_expanded, ncmul))
+                       return dirac_trace(e_expanded, rl);
+
                // gamma5 gets moved to the front so this check is enough
                bool has_gamma5 = is_ex_of_type(e.op(0).op(0), diracgamma5);
                unsigned num = e.nops();
@@ -351,9 +365,28 @@ ex dirac_trace(const ex & e, unsigned char rl = 0)
 
                        // Trace of gamma5 * odd number of gammas and trace of
                        // gamma5 * gamma_mu * gamma_nu are zero
-                       if ((num & 1) == 0 || num == 2)
+                       if ((num & 1) == 0 || num == 3)
                                return _ex0();
 
+                       // Tr gamma5 S_2k =
+                       //   epsilon0123_mu1_mu2_mu3_mu4 * Tr gamma_mu1 gamma_mu2 gamma_mu3 gamma_mu4 S_2k
+                       ex dim = ex_to_idx(e.op(1).op(1)).get_dim();
+                       varidx mu1((new symbol)->setflag(status_flags::dynallocated), dim),
+                              mu2((new symbol)->setflag(status_flags::dynallocated), dim),
+                              mu3((new symbol)->setflag(status_flags::dynallocated), dim),
+                              mu4((new symbol)->setflag(status_flags::dynallocated), dim);
+                       exvector v;
+                       v.reserve(num + 3);
+                       v.push_back(dirac_gamma(mu1, rl));
+                       v.push_back(dirac_gamma(mu2, rl));
+                       v.push_back(dirac_gamma(mu3, rl));
+                       v.push_back(dirac_gamma(mu4, rl));
+                       for (int i=1; i<num; i++)
+                               v.push_back(e.op(i));
+
+                       return (eps0123(mu1.toggle_variance(), mu2.toggle_variance(), mu3.toggle_variance(), mu4.toggle_variance()) *
+                               dirac_trace(ncmul(v), rl)).simplify_indexed() / 24;
+
                } else { // no gamma5
 
                        // Trace of odd number of gammas is zero
@@ -363,9 +396,29 @@ ex dirac_trace(const ex & e, unsigned char rl = 0)
                        // Tr gamma_mu gamma_nu = 4 g_mu_nu
                        if (num == 2)
                                return 4 * lorentz_g(e.op(0).op(1), e.op(1).op(1));
-               }
 
-               throw (std::logic_error("dirac_trace: don't know how to compute trace"));
+                       // Traces of 4 or more gammas are computed recursively:
+                       // Tr gamma_mu1 gamma_mu2 ... gamma_mun =
+                       //   + eta_mu1_mu2 * Tr gamma_mu3 ... gamma_mun
+                       //   - eta_mu1_mu3 * Tr gamma_mu2 gamma_mu4 ... gamma_mun
+                       //   + eta_mu1_mu4 * Tr gamma_mu3 gamma_mu3 gamma_mu5 ... gamma_mun
+                       //   - ...
+                       //   + eta_mu1_mun * Tr gamma_mu2 ... gamma_mu(n-1)
+                       exvector v(num - 2);
+                       int sign = 1;
+                       const ex &ix1 = e.op(0).op(1);
+                       ex result;
+                       for (int i=1; i<num; i++) {
+                               for (int n=1, j=0; n<num; n++) {
+                                       if (n == i)
+                                               continue;
+                                       v[j++] = e.op(n);
+                               }
+                               result += sign * lorentz_g(ix1, e.op(i).op(1)) * dirac_trace(ncmul(v), rl);
+                               sign = -sign;
+                       }
+                       return result;
+               }
        }
 
        return _ex0();