added more trace checks

[ginac.git] / check / exam_clifford.cpp

diff --git a/check/exam_clifford.cpp b/check/exam_clifford.cpp
index 2b28be4c5030636af3e55b83998f4d1fd513de0e..8eee701337931fd94fab5e3f79c4d77812f0d034 100644 (file)
--- a/check/exam_clifford.cpp
+++ b/check/exam_clifford.cpp
@@ -94,6 +94,83 @@ static unsigned clifford_check2(void)
        return result;
 }
 
+static unsigned clifford_check3(void)
+{
+       // checks traces
+
+       unsigned result = 0;
+
+       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);
+       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) * 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 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, 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, 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_slash(l, dim) + dirac_slash(q, dim) + m * dirac_ONE()) *
+           dirac_gamma(mu.toggle_variance()) *
+           (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_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;
+}
+
 unsigned exam_clifford(void)
 {
        unsigned result = 0;
@@ -103,6 +180,7 @@ unsigned exam_clifford(void)
 
        result += clifford_check1();  cout << '.' << flush;
        result += clifford_check2();  cout << '.' << flush;
+       result += clifford_check3();  cout << '.' << flush;
        
        if (!result) {
                cout << " passed " << endl;