* Here we test GiNaC's Clifford algebra objects. */
/*
- * GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
return 0;
}
-static unsigned clifford_check1(void)
+static unsigned clifford_check1()
{
// checks general identities and contractions
return result;
}
-static unsigned clifford_check2(void)
+static unsigned clifford_check2()
{
// checks identities relating to gamma5
return result;
}
-static unsigned clifford_check3(void)
+static unsigned clifford_check3()
{
// checks traces
+ dim * dirac_gamma5() * dirac_gamma(nu) * dirac_gamma(rho) * dirac_gamma(sig) * dirac_gamma(kap);
e = dirac_trace(e).simplify_indexed();
e = (e / (dim - 4)).normal();
- result += check_equal(e, 8 * I * eps0123(nu, rho, sig, kap));
+ result += check_equal(e, 8 * I * lorentz_eps(nu.replace_dim(4), rho.replace_dim(4), sig.replace_dim(4), kap.replace_dim(4)));
// one-loop vacuum polarization in QED
e = dirac_gamma(mu) *
- (dirac_slash(l, dim) + dirac_slash(q, dim) + m * dirac_ONE()) *
+ (dirac_slash(l, dim) + dirac_slash(q, 4) + 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) *
+ e = dirac_slash(q, 4) *
+ (dirac_slash(l, dim) + dirac_slash(q, 4) + m * dirac_ONE()) *
+ dirac_slash(q, 4) *
(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());
+ // stuff that had problems in the past
+ ex prop = dirac_slash(q, dim) - m * dirac_ONE();
+ e = dirac_slash(l, dim) * dirac_gamma5() * dirac_slash(l, dim) * prop;
+ e = dirac_trace(dirac_slash(q, dim) * e) - dirac_trace(m * e)
+ - dirac_trace(prop * e);
+ result += check_equal(e, 0);
+
+ e = (dirac_gamma5() + dirac_ONE()) * dirac_gamma5();
+ e = dirac_trace(e);
+ result += check_equal(e, 4);
+
return result;
}
-static unsigned clifford_check4(void)
+static unsigned clifford_check4()
{
// simplify_indexed()/dirac_trace() cross-checks
return result;
}
-static unsigned clifford_check5(void)
+static unsigned clifford_check5()
{
// canonicalize_clifford() checks
return result;
}
-unsigned exam_clifford(void)
+unsigned exam_clifford()
{
unsigned result = 0;