- dirac_trace() takes an optional third argument: the expression to use for

  the trace of the unit matrix
- more conventional factor I in gamma5

diff --git a/ginac/clifford.cpp b/ginac/clifford.cpp
index 32096410218b76c5cd4c3e179f902faa12b5920e..5c7f7c3b1623e2941131680ed8aa8463f9de2532 100644 (file)
--- a/ginac/clifford.cpp
+++ b/ginac/clifford.cpp
@@ -25,6 +25,7 @@
 #include "idx.h"
 #include "ncmul.h"
 #include "symbol.h"
+#include "numeric.h" // for I
 #include "print.h"
 #include "archive.h"
 #include "debugmsg.h"
@@ -336,13 +337,13 @@ static bool is_clifford_tinfo(unsigned ti, unsigned char rl)
        return ti == (TINFO_clifford + rl);
 }
 
-ex dirac_trace(const ex & e, unsigned char rl)
+ex dirac_trace(const ex & e, unsigned char rl, const ex & trONE)
 {
        if (is_ex_of_type(e, clifford)) {
 
                if (ex_to_clifford(e).get_representation_label() == rl
                 && is_ex_of_type(e.op(0), diracone))
-                       return _ex4();
+                       return trONE;
                else
                        return _ex0();
 
@@ -351,7 +352,7 @@ ex dirac_trace(const ex & e, unsigned char rl)
                // Trace of sum = sum of traces
                ex sum = _ex0();
                for (unsigned i=0; i<e.nops(); i++)
-                       sum += dirac_trace(e.op(i), rl);
+                       sum += dirac_trace(e.op(i), rl, trONE);
                return sum;
 
        } else if (is_ex_exactly_of_type(e, mul)) {
@@ -362,7 +363,7 @@ ex dirac_trace(const ex & e, unsigned char rl)
                        const ex &o = e.op(i);
                        unsigned ti = o.return_type_tinfo();
                        if (is_clifford_tinfo(o.return_type_tinfo(), rl))
-                               prod *= dirac_trace(o, rl);
+                               prod *= dirac_trace(o, rl, trONE);
                        else
                                prod *= o;
                }
@@ -376,7 +377,7 @@ ex dirac_trace(const ex & e, unsigned char rl)
                // Expand product, if necessary
                ex e_expanded = e.expand();
                if (!is_ex_of_type(e_expanded, ncmul))
-                       return dirac_trace(e_expanded, rl);
+                       return dirac_trace(e_expanded, rl, trONE);
 
                // gamma5 gets moved to the front so this check is enough
                bool has_gamma5 = is_ex_of_type(e.op(0).op(0), diracgamma5);
@@ -390,7 +391,7 @@ ex dirac_trace(const ex & e, unsigned char rl)
                                return _ex0();
 
                        // Tr gamma5 S_2k =
-                       //   epsilon0123.mu1.mu2.mu3.mu4 * Tr gamma.mu1 gamma.mu2 gamma.mu3 gamma.mu4 S_2k
+                       //   I/4! * 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),
@@ -406,7 +407,7 @@ ex dirac_trace(const ex & e, unsigned char rl)
                                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;
+                               dirac_trace(ncmul(v), rl, trONE)).simplify_indexed() * I / 24;
 
                } else { // no gamma5
 
@@ -416,7 +417,7 @@ ex dirac_trace(const ex & e, unsigned char rl)
 
                        // 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));
+                               return trONE * lorentz_g(e.op(0).op(1), e.op(1).op(1));
 
                        // Traces of 4 or more gammas are computed recursively:
                        // Tr gamma.mu1 gamma.mu2 ... gamma.mun =
@@ -435,7 +436,7 @@ ex dirac_trace(const ex & e, unsigned char rl)
                                                continue;
                                        v[j++] = e.op(n);
                                }
-                               result += sign * lorentz_g(ix1, e.op(i).op(1)) * dirac_trace(ncmul(v), rl);
+                               result += sign * lorentz_g(ix1, e.op(i).op(1)) * dirac_trace(ncmul(v), rl, trONE);
                                sign = -sign;
                        }
                        return result;

diff --git a/ginac/clifford.h b/ginac/clifford.h
index 69c9e23a6685a3b19f42fbfa17b9bed4113a4431..42be538f5f5bdbe9beb29dd95d67af6ab951b792 100644 (file)
--- a/ginac/clifford.h
+++ b/ginac/clifford.h
@@ -144,8 +144,10 @@ ex dirac_slash(const ex & e, const ex & dim, unsigned char rl = 0);
  *  In particular, the functional is not always cyclic in D != 4 dimensions
  *  when gamma5 is involved.
  *
- *  @param rl Representation label */
-ex dirac_trace(const ex & e, unsigned char rl = 0);
+ *  @param e Expression to take the trace of
+ *  @param rl Representation label
+ *  @param trONE Expression to be returned as the trace of the unit matrix */
+ex dirac_trace(const ex & e, unsigned char rl = 0, const ex & trONE = 4);
 
 
 } // namespace GiNaC

diff --git a/ginac/color.h b/ginac/color.h
index 48903e45ffa5b82737142643543e3776367fc6e8..eb273c71b7da3ec710d5423a3bd2e3fb553a8f0f 100644 (file)
--- a/ginac/color.h
+++ b/ginac/color.h
@@ -157,6 +157,7 @@ ex color_h(const ex & a, const ex & b, const ex & c);
 /** Calculate the trace of an expression containing color objects with a
  *  specified representation label.
  *
+ *  @param e Expression to take the trace of
  *  @param rl Representation label */
 ex color_trace(const ex & e, unsigned char rl = 0);