1 /** @file exam_clifford.cpp
3 * Here we test GiNaC's Clifford algebra objects. */
6 * GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
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13 * This program is distributed in the hope that it will be useful,
14 * but WITHOUT ANY WARRANTY; without even the implied warranty of
15 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
16 * GNU General Public License for more details.
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20 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
25 static unsigned check_equal(const ex &e1, const ex &e2)
29 clog << e1 << "-" << e2 << " erroneously returned "
30 << e << " instead of 0" << endl;
36 static unsigned check_equal_simplify(const ex &e1, const ex &e2)
38 ex e = simplify_indexed(e1) - e2;
40 clog << "simplify_indexed(" << e1 << ")-" << e2 << " erroneously returned "
41 << e << " instead of 0" << endl;
47 static unsigned clifford_check1(void)
49 // checks general identities and contractions
54 varidx mu(symbol("mu"), dim), nu(symbol("nu"), dim);
57 e = dirac_ONE() * dirac_ONE();
58 result += check_equal(e, dirac_ONE());
60 e = dirac_ONE() * dirac_gamma(mu) * dirac_ONE();
61 result += check_equal(e, dirac_gamma(mu));
63 e = dirac_gamma(varidx(2, dim)) * dirac_gamma(varidx(1, dim)) *
64 dirac_gamma(varidx(1, dim)) * dirac_gamma(varidx(2, dim));
65 result += check_equal(e, dirac_ONE());
67 e = dirac_gamma(mu) * dirac_gamma(nu) *
68 dirac_gamma(nu.toggle_variance()) * dirac_gamma(mu.toggle_variance());
69 result += check_equal_simplify(e, pow(dim, 2) * dirac_ONE());
71 e = dirac_gamma(mu) * dirac_gamma(nu) *
72 dirac_gamma(mu.toggle_variance()) * dirac_gamma(nu.toggle_variance());
73 result += check_equal_simplify(e, 2*dim*dirac_ONE()-pow(dim, 2)*dirac_ONE());
78 static unsigned clifford_check2(void)
80 // checks identities relating to gamma5
85 varidx mu(symbol("mu"), dim), nu(symbol("nu"), dim);
88 e = dirac_gamma(mu) * dirac_gamma5() + dirac_gamma5() * dirac_gamma(mu);
89 result += check_equal(e, 0);
91 e = dirac_gamma5() * dirac_gamma(mu) * dirac_gamma5() + dirac_gamma(mu);
92 result += check_equal(e, 0);
97 static unsigned clifford_check3(void)
103 symbol dim("D"), m("m"), q("q"), l("l"), ldotq("ldotq");
104 varidx mu(symbol("mu"), dim), nu(symbol("nu"), dim), rho(symbol("rho"), dim),
105 sig(symbol("sig"), dim), kap(symbol("kap"), dim), lam(symbol("lam"), 4);
109 sp.add(q, q, pow(q, 2));
110 sp.add(l, l, pow(l, 2));
113 e = pow(m, 2) * indexed(q, mu) * indexed(q, nu)
114 * dirac_gamma(mu.toggle_variance()) * dirac_gamma(nu.toggle_variance());
115 e = dirac_trace(e).simplify_indexed(sp);
116 result += check_equal(e, 4*pow(m, 2)*pow(q, 2));
119 e = dirac_gamma(mu) * dirac_gamma(nu) * dirac_gamma(rho) * dirac_gamma(sig)
120 - dirac_gamma(nu) * dirac_gamma(rho) * dirac_gamma(sig) * dirac_gamma(mu);
122 result += check_equal(e.expand(), 0);
124 e = dirac_gamma(mu) * dirac_gamma(nu) * dirac_gamma(rho) * dirac_gamma(sig) * dirac_gamma(kap) * dirac_gamma(lam)
125 - dirac_gamma(nu) * dirac_gamma(rho) * dirac_gamma(sig) * dirac_gamma(kap) * dirac_gamma(lam) * dirac_gamma(mu);
127 result += check_equal(e.expand(), 0);
129 // one-loop vacuum polarization in QED
130 e = dirac_gamma(mu) *
131 (dirac_gamma(nu) * indexed(l, nu.toggle_variance()) + dirac_gamma(nu) * indexed(q, nu.toggle_variance()) + m * dirac_ONE()) *
132 dirac_gamma(mu.toggle_variance()) *
133 (dirac_gamma(rho) * indexed(l, rho.toggle_variance()) + m * dirac_ONE());
134 e = dirac_trace(e.expand()).simplify_indexed(sp);
135 result += check_equal(e, 4*((2-dim)*l*l + (2-dim)*ldotq + dim*m*m).expand());
137 e = dirac_gamma(mu) * indexed(q, mu.toggle_variance()) *
138 (dirac_gamma(nu) * indexed(l, nu.toggle_variance()) + dirac_gamma(nu) * indexed(q, nu.toggle_variance()) + m * dirac_ONE()) *
139 dirac_gamma(sig) * indexed(q, sig.toggle_variance()) *
140 (dirac_gamma(rho) * indexed(l, rho.toggle_variance()) + m * dirac_ONE());
141 e = dirac_trace(e.expand()).simplify_indexed(sp);
142 result += check_equal(e, 4*(2*ldotq*ldotq + q*q*ldotq - q*q*l*l + q*q*m*m).expand());
147 unsigned exam_clifford(void)
151 cout << "examining clifford objects" << flush;
152 clog << "----------clifford objects:" << endl;
154 result += clifford_check1(); cout << '.' << flush;
155 result += clifford_check2(); cout << '.' << flush;
156 result += clifford_check3(); cout << '.' << flush;
159 cout << " passed " << endl;
160 clog << "(no output)" << endl;
162 cout << " failed " << endl;