varidx mu(symbol("mu"), dim), nu(symbol("nu"), dim);
ex e;
+ e = dirac_ONE() * dirac_ONE();
+ result += check_equal(e, dirac_ONE());
+
+ e = dirac_ONE() * dirac_gamma(mu) * dirac_ONE();
+ result += check_equal(e, dirac_gamma(mu));
+
+ e = dirac_gamma(varidx(2, dim)) * dirac_gamma(varidx(1, dim)) *
+ dirac_gamma(varidx(1, dim)) * dirac_gamma(varidx(2, dim));
+ result += check_equal(e, dirac_ONE());
+
e = dirac_gamma(mu) * dirac_gamma(nu) *
dirac_gamma(nu.toggle_variance()) * dirac_gamma(mu.toggle_variance());
- result += check_equal_simplify(e, pow(dim, 2) * dirac_one());
+ result += check_equal_simplify(e, pow(dim, 2) * dirac_ONE());
e = dirac_gamma(mu) * dirac_gamma(nu) *
dirac_gamma(mu.toggle_variance()) * dirac_gamma(nu.toggle_variance());
- result += check_equal_simplify(e, 2*dim*dirac_one()-pow(dim, 2)*dirac_one());
+ result += check_equal_simplify(e, 2*dim*dirac_ONE()-pow(dim, 2)*dirac_ONE());
+
+ return result;
+}
+
+static unsigned clifford_check2(void)
+{
+ // checks identities relating to gamma5
+
+ unsigned result = 0;
+
+ symbol dim("D");
+ varidx mu(symbol("mu"), dim), nu(symbol("nu"), dim);
+ ex e;
+
+ e = dirac_gamma(mu) * dirac_gamma5() + dirac_gamma5() * dirac_gamma(mu);
+ result += check_equal(e, 0);
+
+ e = dirac_gamma5() * dirac_gamma(mu) * dirac_gamma5() + dirac_gamma(mu);
+ result += check_equal(e, 0);
+
+ return result;
+}
+
+static unsigned clifford_check3(void)
+{
+ // checks traces
+
+ unsigned result = 0;
+
+ symbol dim("D"), m("m"), q("q");
+ varidx mu(symbol("mu"), dim), nu(symbol("nu"), dim);
+ scalar_products sp;
+ ex e;
+
+ sp.add(q, q, pow(q, 2));
+
+ e = pow(m, 2) * indexed(q, mu) * indexed(q, nu)
+ * dirac_gamma(mu.toggle_variance()) * dirac_gamma(nu.toggle_variance());
+ e = dirac_trace(e).simplify_indexed(sp);
+ result += check_equal(e, 4*pow(m, 2)*pow(q, 2));
return result;
}
clog << "----------clifford objects:" << endl;
result += clifford_check1(); cout << '.' << flush;
+ result += clifford_check2(); cout << '.' << flush;
+ result += clifford_check3(); cout << '.' << flush;
if (!result) {
cout << " passed " << endl;