added more trace checks

diff --git a/check/exam_clifford.cpp b/check/exam_clifford.cpp
index 19b4e822c34432536932dd4ace1344bdb1b7ae62..8eee701337931fd94fab5e3f79c4d77812f0d034 100644 (file)
--- a/check/exam_clifford.cpp
+++ b/check/exam_clifford.cpp
@@ -103,42 +103,69 @@ static unsigned clifford_check3(void)
        symbol dim("D"), m("m"), q("q"), l("l"), ldotq("ldotq");
        varidx mu(symbol("mu"), dim), nu(symbol("nu"), dim), rho(symbol("rho"), dim),
               sig(symbol("sig"), dim), kap(symbol("kap"), dim), lam(symbol("lam"), 4);
-       scalar_products sp;
        ex e;
 
+       e = dirac_gamma(mu);
+       result += check_equal(dirac_trace(e), 0);
+
+       e = dirac_gamma(mu) * dirac_gamma(nu) * dirac_gamma(rho);
+       result += check_equal(dirac_trace(e), 0);
+
+       e = dirac_gamma5() * dirac_gamma(mu);
+       result += check_equal(dirac_trace(e), 0);
+
+       e = dirac_gamma5() * dirac_gamma(mu) * dirac_gamma(nu);
+       result += check_equal(dirac_trace(e), 0);
+
+       e = dirac_gamma5() * dirac_gamma(mu) * dirac_gamma(nu) * dirac_gamma(rho);
+       result += check_equal(dirac_trace(e), 0);
+
+       scalar_products sp;
        sp.add(q, q, pow(q, 2));
        sp.add(l, l, pow(l, 2));
        sp.add(l, q, ldotq);
 
-       e = pow(m, 2) * indexed(q, mu) * indexed(q, nu)
-         * dirac_gamma(mu.toggle_variance()) * dirac_gamma(nu.toggle_variance());
+       e = pow(m, 2) * dirac_slash(q, dim) * dirac_slash(q, dim);
        e = dirac_trace(e).simplify_indexed(sp);
        result += check_equal(e, 4*pow(m, 2)*pow(q, 2));
 
-       // cyclicity
+       // cyclicity without gamma5
        e = dirac_gamma(mu) * dirac_gamma(nu) * dirac_gamma(rho) * dirac_gamma(sig)
          - dirac_gamma(nu) * dirac_gamma(rho) * dirac_gamma(sig) * dirac_gamma(mu);
        e = dirac_trace(e);
-       result += check_equal(e.expand(), 0);
+       result += check_equal(e, 0);
 
        e = dirac_gamma(mu) * dirac_gamma(nu) * dirac_gamma(rho) * dirac_gamma(sig) * dirac_gamma(kap) * dirac_gamma(lam)
          - dirac_gamma(nu) * dirac_gamma(rho) * dirac_gamma(sig) * dirac_gamma(kap) * dirac_gamma(lam) * dirac_gamma(mu);
+       e = dirac_trace(e).expand();
+       result += check_equal(e, 0);
+
+       // cyclicity of gamma5 * S_4
+       e = dirac_gamma5() * dirac_gamma(mu) * dirac_gamma(nu) * dirac_gamma(rho) * dirac_gamma(sig)
+         - dirac_gamma(sig) * dirac_gamma5() * dirac_gamma(mu) * dirac_gamma(nu) * dirac_gamma(rho);
        e = dirac_trace(e);
-       result += check_equal(e.expand(), 0);
+       result += check_equal(e, 0);
+
+       // non-cyclicity of order D-4 of gamma5 * S_6
+       e = dirac_gamma5() * dirac_gamma(mu) * dirac_gamma(nu) * dirac_gamma(rho) * dirac_gamma(sig) * dirac_gamma(kap) * dirac_gamma(mu.toggle_variance())
+         + dim * dirac_gamma5() * dirac_gamma(nu) * dirac_gamma(rho) * dirac_gamma(sig) * dirac_gamma(kap);
+       e = dirac_trace(e);
+       e = (e / (dim - 4)).normal();
+       result += check_equal(e, 8 * eps0123(nu, rho, sig, kap));
 
        // one-loop vacuum polarization in QED
        e = dirac_gamma(mu) *
-           (dirac_gamma(nu) * indexed(l, nu.toggle_variance()) + dirac_gamma(nu) * indexed(q, nu.toggle_variance()) + m * dirac_ONE()) *
+           (dirac_slash(l, dim) + dirac_slash(q, dim) + m * dirac_ONE()) *
            dirac_gamma(mu.toggle_variance()) *
-           (dirac_gamma(rho) * indexed(l, rho.toggle_variance()) + m * dirac_ONE());
-       e = dirac_trace(e.expand()).simplify_indexed(sp);
+           (dirac_slash(l, dim) + m * dirac_ONE());
+       e = dirac_trace(e).simplify_indexed(sp);
        result += check_equal(e, 4*((2-dim)*l*l + (2-dim)*ldotq + dim*m*m).expand());
 
-    e = dirac_gamma(mu) * indexed(q, mu.toggle_variance()) *
-           (dirac_gamma(nu) * indexed(l, nu.toggle_variance()) + dirac_gamma(nu) * indexed(q, nu.toggle_variance()) + m * dirac_ONE()) *
-           dirac_gamma(sig) * indexed(q, sig.toggle_variance()) *
-           (dirac_gamma(rho) * indexed(l, rho.toggle_variance()) + m * dirac_ONE());
-       e = dirac_trace(e.expand()).simplify_indexed(sp);
+       e = dirac_slash(q, dim) *
+           (dirac_slash(l, dim) + dirac_slash(q, dim) + m * dirac_ONE()) *
+           dirac_slash(q, dim) *
+           (dirac_slash(l, dim) + m * dirac_ONE());
+       e = dirac_trace(e).simplify_indexed(sp);
        result += check_equal(e, 4*(2*ldotq*ldotq + q*q*ldotq - q*q*l*l + q*q*m*m).expand());
 
        return result;