- Clifford traces of many gammas are a lot faster now (especially with gamma5)

[ginac.git] / ginac / clifford.cpp

diff --git a/ginac/clifford.cpp b/ginac/clifford.cpp
index bd0c896196a6ec0c067758d110a0398a2c45b57b..d520822d6d8d3e38aed5699321434ef021c8e559 100644 (file)
--- a/ginac/clifford.cpp
+++ b/ginac/clifford.cpp
@@ -389,24 +389,62 @@ ex dirac_trace(const ex & e, unsigned char rl, const ex & trONE)
                        if ((num & 1) == 0 || num == 3)
                                return _ex0();
 
+                       // Tr gamma5 gamma.mu gamma.nu gamma.rho gamma.sigma = 4I * epsilon(mu, nu, rho, sigma)
+                       if (num == 5)
+                               return trONE * I * eps0123(e.op(1).op(1), e.op(2).op(1), e.op(3).op(1), e.op(4).op(1));
+
+                       // Tr gamma5 gamma.mu1 gamma.mu2 gamma.mu3 gamma.mu4 gamma.mu5 gamma.mu6 = ...
+                       if (num == 7) {
+                               ex i1 = e.op(1).op(1), i2 = e.op(2).op(1),
+                                  i3 = e.op(3).op(1), i4 = e.op(4).op(1),
+                                  i5 = e.op(5).op(1), i6 = e.op(6).op(1);
+                               return trONE * I * (lorentz_g(i1, i2) * eps0123(i3, i4, i5, i6)
+                                                 - lorentz_g(i1, i3) * eps0123(i2, i4, i5, i6)
+                                                 + lorentz_g(i1, i4) * eps0123(i2, i3, i5, i6)
+                                                 - lorentz_g(i1, i5) * eps0123(i2, i3, i4, i6)
+                                                 + lorentz_g(i1, i6) * eps0123(i2, i3, i4, i5)
+                                                 + lorentz_g(i2, i3) * eps0123(i1, i4, i5, i6)
+                                                 - lorentz_g(i2, i4) * eps0123(i1, i3, i5, i6)
+                                                 + lorentz_g(i2, i5) * eps0123(i1, i3, i4, i6)
+                                                 - lorentz_g(i2, i6) * eps0123(i1, i3, i4, i5)
+                                                 + lorentz_g(i3, i4) * eps0123(i1, i2, i5, i6)
+                                                 - lorentz_g(i3, i5) * eps0123(i1, i2, i4, i6)
+                                                 + lorentz_g(i3, i6) * eps0123(i1, i2, i4, i5)
+                                                 + lorentz_g(i4, i5) * eps0123(i1, i2, i3, i6)
+                                                 - lorentz_g(i4, i6) * eps0123(i1, i2, i3, i5)
+                                                 + lorentz_g(i5, i6) * eps0123(i1, i2, i3, i4));
+                       }
+
                        // Tr gamma5 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),
-                              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, trONE)).simplify_indexed() * I / 24;
+                       ex result;
+                       for (int i=1; i<num-3; i++) {
+                               ex idx1 = e.op(i).op(1);
+                               for (int j=i+1; j<num-2; j++) {
+                                       ex idx2 = e.op(j).op(1);
+                                       for (int k=j+1; k<num-1; k++) {
+                                               ex idx3 = e.op(k).op(1);
+                                               for (int l=k+1; l<num; l++) {
+                                                       ex idx4 = e.op(l).op(1);
+                                                       vector<int> iv;
+                                                       iv.reserve(num-1);
+                                                       exvector v;
+                                                       v.reserve(num-1);
+                                                       iv.push_back(i); iv.push_back(j); iv.push_back(k); iv.push_back(l);
+                                                       for (int n=1; n<num; n++) {
+                                                               if (n == i || n == j || n == k || n == l)
+                                                                       continue;
+                                                               iv.push_back(n);
+                                                               v.push_back(e.op(n));
+                                                       }
+                                                       int sign = permutation_sign(iv);
+                                                       result += sign * eps0123(idx1, idx2, idx3, idx4)
+                                                               * dirac_trace(ncmul(v), rl, trONE);
+                                               }
+                                       }
+                               }
+                       }
+                       return result * I;
 
                } else { // no gamma5
 
@@ -418,7 +456,13 @@ ex dirac_trace(const ex & e, unsigned char rl, const ex & trONE)
                        if (num == 2)
                                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.mu gamma.nu gamma.rho gamma.sig = 4 (g.mu.nu g.rho.sig + g.nu.rho g.mu.sig - g.mu.rho g.nu.sig
+                       if (num == 4)
+                               return trONE * (lorentz_g(e.op(0).op(1), e.op(1).op(1)) * lorentz_g(e.op(2).op(1), e.op(3).op(1))
+                                             + lorentz_g(e.op(1).op(1), e.op(2).op(1)) * lorentz_g(e.op(0).op(1), e.op(3).op(1))
+                                             - lorentz_g(e.op(0).op(1), e.op(2).op(1)) * lorentz_g(e.op(1).op(1), e.op(3).op(1)));
+
+                       // Traces of 6 or more gammas are computed recursively:
                        // Tr gamma.mu1 gamma.mu2 ... gamma.mun =
                        //   + g.mu1.mu2 * Tr gamma.mu3 ... gamma.mun
                        //   - g.mu1.mu3 * Tr gamma.mu2 gamma.mu4 ... gamma.mun