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

[ginac.git] / ginac / clifford.cpp

diff --git a/ginac/clifford.cpp b/ginac/clifford.cpp
index 5a69cfd58db038073f36bd1728d96edbb5a222f8..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"
@@ -178,20 +179,6 @@ bool diracgamma::contract_with(exvector::iterator self, exvector::iterator other
                        *other = _ex1();
                        return true;
 
-#if 0
-               // gamma~mu gamma~alpha gamma~beta gamma~delta gamma.mu = -2 gamma~delta gamma~beta gamma~alpha + (4-dim) gamma~alpha gamma~beta gamma~delta
-               } else if (other - self == 4
-                       && is_ex_of_type(self[1], clifford)
-                       && is_ex_of_type(self[2], clifford)
-                       && is_ex_of_type(self[3], clifford)) {
-                       *self = -2 * self[3] * self[2] * self[1] + (4 - dim) * self[1] * self[2] * self[3];
-                       self[1] = _ex1();
-                       self[2] = _ex1();
-                       self[3] = _ex1();
-                       *other = _ex1();
-                       return true;
-#endif
-
                // gamma~mu S gamma~alpha gamma.mu = 2 gamma~alpha S - gamma~mu S gamma.mu gamma~alpha
                // (commutate contracted indices towards each other, simplify_indexed()
                // will re-expand and re-run the simplification)
@@ -327,6 +314,16 @@ ex dirac_gamma5(unsigned char rl)
        return clifford(diracgamma5(), rl);
 }
 
+ex dirac_gamma6(unsigned char rl)
+{
+       return clifford(diracone(), rl) + clifford(diracgamma5(), rl);
+}
+
+ex dirac_gamma7(unsigned char rl)
+{
+       return clifford(diracone(), rl) - clifford(diracgamma5(), rl);
+}
+
 ex dirac_slash(const ex & e, const ex & dim, unsigned char rl)
 {
        varidx mu((new symbol)->setflag(status_flags::dynallocated), dim);
@@ -340,13 +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();
 
@@ -355,7 +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)) {
@@ -366,7 +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;
                }
@@ -380,7 +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);
@@ -394,7 +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),
@@ -410,7 +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
 
@@ -420,7 +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 =
@@ -439,7 +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;