From d81773c9ebc817764485203f4892607a98667d48 Mon Sep 17 00:00:00 2001 From: Christian Bauer Date: Thu, 26 Apr 2001 19:33:22 +0000 Subject: [PATCH 1/1] added more trace checks --- check/exam_clifford.cpp | 55 ++++++++++++++++++++++++++++++----------- 1 file changed, 41 insertions(+), 14 deletions(-) diff --git a/check/exam_clifford.cpp b/check/exam_clifford.cpp index 19b4e822..8eee7013 100644 --- a/check/exam_clifford.cpp +++ b/check/exam_clifford.cpp @@ -103,42 +103,69 @@ static unsigned clifford_check3(void) 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); - scalar_products sp; 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) * indexed(q, mu) * indexed(q, nu) - * dirac_gamma(mu.toggle_variance()) * dirac_gamma(nu.toggle_variance()); + 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 + // 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.expand(), 0); + 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.expand(), 0); + 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_gamma(nu) * indexed(l, nu.toggle_variance()) + dirac_gamma(nu) * indexed(q, nu.toggle_variance()) + m * dirac_ONE()) * + (dirac_slash(l, dim) + dirac_slash(q, dim) + m * dirac_ONE()) * dirac_gamma(mu.toggle_variance()) * - (dirac_gamma(rho) * indexed(l, rho.toggle_variance()) + m * dirac_ONE()); - e = dirac_trace(e.expand()).simplify_indexed(sp); + (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_gamma(mu) * indexed(q, mu.toggle_variance()) * - (dirac_gamma(nu) * indexed(l, nu.toggle_variance()) + dirac_gamma(nu) * indexed(q, nu.toggle_variance()) + m * dirac_ONE()) * - dirac_gamma(sig) * indexed(q, sig.toggle_variance()) * - (dirac_gamma(rho) * indexed(l, rho.toggle_variance()) + m * dirac_ONE()); - e = dirac_trace(e.expand()).simplify_indexed(sp); + 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; -- 2.44.0