From 3acbd48bb5396559a85cfebb338f382126d8adc4 Mon Sep 17 00:00:00 2001 From: Christian Bauer Date: Wed, 25 Apr 2001 20:40:35 +0000 Subject: [PATCH 1/1] added more trace checks --- check/exam_clifford.cpp | 33 +++++++++++++++++++++++++++++++-- 1 file changed, 31 insertions(+), 2 deletions(-) diff --git a/check/exam_clifford.cpp b/check/exam_clifford.cpp index 6f1540a7..19b4e822 100644 --- a/check/exam_clifford.cpp +++ b/check/exam_clifford.cpp @@ -100,18 +100,47 @@ static unsigned clifford_check3(void) unsigned result = 0; - symbol dim("D"), m("m"), q("q"); - varidx mu(symbol("mu"), dim), nu(symbol("nu"), dim); + 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; 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 = dirac_trace(e).simplify_indexed(sp); result += check_equal(e, 4*pow(m, 2)*pow(q, 2)); + // cyclicity + 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); + + 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); + result += check_equal(e.expand(), 0); + + // 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_gamma(mu.toggle_variance()) * + (dirac_gamma(rho) * indexed(l, rho.toggle_variance()) + m * dirac_ONE()); + e = dirac_trace(e.expand()).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); + 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