* epsilon_tensor(idx(fail(), 3), idx(0, 3), idx(y/2, 3))
+ lorentz_g(
varidx(lst(x, -11*y, acos(2*x).series(x==3-5*I, 3)) * color_ONE()
- * metric_tensor(varidx(0, 5), varidx(2, 4)), zeta(3)),
+ * metric_tensor(spinidx(0, 5, false, true), varidx(2, 4)), zeta(3)),
varidx(diag_matrix(lst(-1, Euler, atan(x/y==-15*I/17)))
* delta_tensor(idx(x, 2), idx(y, 3)), log(cos(128.0/(x*y))), true),
true
static unsigned color_check1(void)
{
- // checks general identities and contractions
+ // checks general identities and contractions of the structure constants
unsigned result = 0;
idx a(symbol("a"), 8), b(symbol("b"), 8), c(symbol("c"), 8), d(symbol("d"), 8);
- // structure constants
result += check_equal(color_d(a, c, a), 0);
result += check_equal_simplify(color_d(a, b, c) * color_d(b, d, c), numeric(5,3) * delta_tensor(a, d));
result += check_equal_simplify(color_d(idx(5, 8), b, c) * color_d(b, idx(5, 8), c), numeric(5,3));
return result;
}
+static unsigned color_check2(void)
+{
+ // checks general identities and contractions of the generators
+
+ unsigned result = 0;
+
+ idx a(symbol("a"), 8), b(symbol("b"), 8), c(symbol("c"), 8), k(symbol("k"), 8);
+ ex e;
+
+ e = color_T(k) * color_T(k);
+ result += check_equal_simplify(e, 4 * color_ONE() / 3);
+ e = color_T(k) * color_T(a) * color_T(k);
+ result += check_equal_simplify(e, -color_T(a) / 6);
+ e = color_T(k) * color_T(a) * color_T(b) * color_T(k);
+ result += check_equal_simplify(e, delta_tensor(a, b) * color_ONE() / 4 - color_T(a) * color_T(b) / 6);
+ e = color_T(k) * color_T(a) * color_T(b) * color_T(c) * color_T(k);
+ result += check_equal_simplify(e, (color_h(a, b, c) * color_ONE() / 8).expand() - color_T(a) * color_T(b) * color_T(c) / 6);
+ e = color_T(a) * color_T(b) * color_T(a) * color_T(b);
+ result += check_equal_simplify(e, -2 * color_ONE() / 9);
+ e = color_T(a) * color_T(b) * color_T(b) * color_T(a);
+ result += check_equal_simplify(e, 16 * color_ONE() / 9);
+ e = color_T(a) * color_T(b) * color_T(c) * color_T(c) * color_T(b) * color_T(a);
+ result += check_equal_simplify(e, 64 * color_ONE() / 27);
+
+ return result;
+}
+
+static unsigned color_check3(void)
+{
+ // checks traces
+
+ unsigned result = 0;
+
+ idx a(symbol("a"), 8), b(symbol("b"), 8), c(symbol("c"), 8), k(symbol("k"), 8);
+ ex e;
+
+ e = color_ONE();
+ result += check_equal(color_trace(e), 3);
+ e = color_T(a);
+ result += check_equal(color_trace(e), 0);
+ e = color_T(a) * color_T(b);
+ result += check_equal(color_trace(e), delta_tensor(a, b) / 2);
+ e = color_T(a) * color_T(b) * color_T(c);
+ result += check_equal(color_trace(e), color_h(a, b, c) / 4);
+
+ return result;
+}
+
unsigned exam_color(void)
{
unsigned result = 0;
clog << "----------color objects:" << endl;
result += color_check1(); cout << '.' << flush;
+ result += color_check2(); cout << '.' << flush;
+ result += color_check3(); cout << '.' << flush;
if (!result) {
cout << " passed " << endl;
return result;
}
+static unsigned spinor_check(void)
+{
+ // check identities of the spinor metric
+
+ unsigned result = 0;
+
+ symbol psi("psi");
+ spinidx A(symbol("A"), 2), B(symbol("B"), 2), C(symbol("C"), 2);
+ ex A_co = A.toggle_variance(), B_co = B.toggle_variance();
+ ex e;
+
+ e = spinor_metric(A_co, B_co) * spinor_metric(A, B);
+ result += check_equal_simplify(e, 2);
+ e = spinor_metric(A_co, B_co) * spinor_metric(B, A);
+ result += check_equal_simplify(e, -2);
+ e = spinor_metric(A_co, B_co) * spinor_metric(A, C);
+ result += check_equal_simplify(e, delta_tensor(B_co, C));
+ e = spinor_metric(A_co, B_co) * spinor_metric(B, C);
+ result += check_equal_simplify(e, -delta_tensor(A_co, C));
+ e = spinor_metric(A_co, B_co) * spinor_metric(C, A);
+ result += check_equal_simplify(e, -delta_tensor(B_co, C));
+ e = spinor_metric(A, B) * indexed(psi, B_co);
+ result += check_equal_simplify(e, indexed(psi, A));
+ e = spinor_metric(A, B) * indexed(psi, A_co);
+ result += check_equal_simplify(e, -indexed(psi, B));
+ e = spinor_metric(A_co, B_co) * indexed(psi, B);
+ result += check_equal_simplify(e, -indexed(psi, A_co));
+ e = spinor_metric(A_co, B_co) * indexed(psi, A);
+ result += check_equal_simplify(e, indexed(psi, B_co));
+
+ return result;
+}
+
unsigned exam_indexed(void)
{
unsigned result = 0;
result += symmetry_check(); cout << '.' << flush;
result += scalar_product_check(); cout << '.' << flush;
result += edyn_check(); cout << '.' << flush;
+ result += spinor_check(); cout << '.' << flush;
if (!result) {
cout << " passed " << endl;