X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=check%2Fexam_clifford.cpp;h=8eee701337931fd94fab5e3f79c4d77812f0d034;hp=2b28be4c5030636af3e55b83998f4d1fd513de0e;hb=d81773c9ebc817764485203f4892607a98667d48;hpb=2e13bfeb92ce55b3ee7e24cc6041f70c7a0eff4e

diff --git a/check/exam_clifford.cpp b/check/exam_clifford.cpp
index 2b28be4c..8eee7013 100644
--- 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;