GINAC_IMPLEMENT_REGISTERED_CLASS(tensdelta, tensor)
GINAC_IMPLEMENT_REGISTERED_CLASS(tensmetric, tensor)
GINAC_IMPLEMENT_REGISTERED_CLASS(minkmetric, tensmetric)
+GINAC_IMPLEMENT_REGISTERED_CLASS(spinmetric, tensmetric)
GINAC_IMPLEMENT_REGISTERED_CLASS(tensepsilon, tensor)
//////////
DEFAULT_CTORS(tensor)
DEFAULT_CTORS(tensdelta)
DEFAULT_CTORS(tensmetric)
+DEFAULT_COPY(spinmetric)
+DEFAULT_DESTROY(spinmetric)
DEFAULT_DESTROY(minkmetric)
DEFAULT_DESTROY(tensepsilon)
tinfo_key = TINFO_minkmetric;
}
+spinmetric::spinmetric()
+{
+ debugmsg("spinmetric default constructor", LOGLEVEL_CONSTRUCT);
+ tinfo_key = TINFO_spinmetric;
+}
+
minkmetric::minkmetric(bool ps) : pos_sig(ps)
{
debugmsg("minkmetric constructor from bool", LOGLEVEL_CONSTRUCT);
DEFAULT_ARCHIVING(tensor)
DEFAULT_ARCHIVING(tensdelta)
DEFAULT_ARCHIVING(tensmetric)
+DEFAULT_ARCHIVING(spinmetric)
DEFAULT_UNARCHIVE(minkmetric)
DEFAULT_UNARCHIVE(tensepsilon)
DEFAULT_COMPARE(tensor)
DEFAULT_COMPARE(tensdelta)
DEFAULT_COMPARE(tensmetric)
+DEFAULT_COMPARE(spinmetric)
int minkmetric::compare_same_type(const basic & other) const
{
DEFAULT_PRINT_LATEX(tensdelta, "delta", "\\delta")
DEFAULT_PRINT(tensmetric, "g")
DEFAULT_PRINT_LATEX(minkmetric, "eta", "\\eta")
-DEFAULT_PRINT_LATEX(tensepsilon, "eps", "\\epsilon")
+DEFAULT_PRINT_LATEX(spinmetric, "eps", "\\varepsilon")
+DEFAULT_PRINT_LATEX(tensepsilon, "eps", "\\varepsilon")
/** Automatic symbolic evaluation of an indexed delta tensor. */
ex tensdelta::eval_indexed(const basic & i) const
return inherited::eval_indexed(i);
}
+/** Automatic symbolic evaluation of an indexed metric tensor. */
+ex spinmetric::eval_indexed(const basic & i) const
+{
+ GINAC_ASSERT(is_of_type(i, indexed));
+ GINAC_ASSERT(i.nops() == 3);
+ GINAC_ASSERT(is_ex_of_type(i.op(0), spinmetric));
+ GINAC_ASSERT(is_ex_of_type(i.op(1), spinidx));
+ GINAC_ASSERT(is_ex_of_type(i.op(2), spinidx));
+
+ const spinidx & i1 = ex_to_spinidx(i.op(1));
+ const spinidx & i2 = ex_to_spinidx(i.op(2));
+
+ // Convolutions are zero
+ if (static_cast<const indexed &>(i).get_dummy_indices().size() != 0)
+ return _ex0();
+
+ // Numeric evaluation
+ if (static_cast<const indexed &>(i).all_index_values_are(info_flags::nonnegint)) {
+ int n1 = ex_to_numeric(i1.get_value()).to_int(), n2 = ex_to_numeric(i2.get_value()).to_int();
+ if (n1 == n2)
+ return _ex0();
+ else if (n1 < n2)
+ return _ex1();
+ else
+ return _ex_1();
+ }
+
+ // No further simplifications
+ return i.hold();
+}
+
/** Automatic symbolic evaluation of an indexed epsilon tensor. */
ex tensepsilon::eval_indexed(const basic & i) const
{
return false;
}
+/** Contraction of an indexed spinor metric with something else. */
+bool spinmetric::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
+{
+ GINAC_ASSERT(is_ex_of_type(*self, indexed));
+ GINAC_ASSERT(is_ex_of_type(*other, indexed));
+ GINAC_ASSERT(self->nops() == 3);
+ GINAC_ASSERT(is_ex_of_type(self->op(0), spinmetric));
+
+ // Contractions between spinor metrics
+ if (is_ex_of_type(other->op(0), spinmetric)) {
+ const idx &self_i1 = ex_to_idx(self->op(1));
+ const idx &self_i2 = ex_to_idx(self->op(2));
+ const idx &other_i1 = ex_to_idx(other->op(1));
+ const idx &other_i2 = ex_to_idx(other->op(2));
+
+ if (is_dummy_pair(self_i1, other_i1)) {
+ if (is_dummy_pair(self_i2, other_i2))
+ *self = _ex2();
+ else
+ *self = delta_tensor(self_i2, other_i2);
+ *other = _ex1();
+ return true;
+ } else if (is_dummy_pair(self_i1, other_i2)) {
+ if (is_dummy_pair(self_i2, other_i1))
+ *self = _ex_2();
+ else
+ *self = -delta_tensor(self_i2, other_i1);
+ *other = _ex1();
+ return true;
+ } else if (is_dummy_pair(self_i2, other_i1)) {
+ *self = -delta_tensor(self_i1, other_i2);
+ *other = _ex1();
+ return true;
+ } else if (is_dummy_pair(self_i2, other_i2)) {
+ *self = delta_tensor(self_i1, other_i1);
+ *other = _ex1();
+ return true;
+ }
+ }
+
+ // If contracting with the delta tensor, let the delta do it
+ // (don't raise/lower delta indices)
+ if (is_ex_of_type(other->op(0), tensdelta))
+ return false;
+
+ // Try to contract first index
+ const idx *self_idx = &ex_to_idx(self->op(1));
+ const idx *free_idx = &ex_to_idx(self->op(2));
+ bool first_index_tried = false;
+ int sign = 1;
+
+again:
+ if (self_idx->is_symbolic()) {
+ for (int i=1; i<other->nops(); i++) {
+ const idx &other_idx = ex_to_idx(other->op(i));
+ if (is_dummy_pair(*self_idx, other_idx)) {
+
+ // Contraction found, remove metric tensor and substitute
+ // index in second object
+ *self = (static_cast<const spinidx *>(self_idx)->is_covariant() ? sign : -sign);
+ *other = other->subs(other_idx == *free_idx);
+ return true;
+ }
+ }
+ }
+
+ if (!first_index_tried) {
+
+ // No contraction with first index found, try second index
+ self_idx = &ex_to_idx(self->op(2));
+ free_idx = &ex_to_idx(self->op(1));
+ first_index_tried = true;
+ sign = -sign;
+ goto again;
+ }
+
+ return false;
+}
+
//////////
// global functions
//////////
return indexed(minkmetric(pos_sig), indexed::symmetric, i1, i2);
}
+ex spinor_metric(const ex & i1, const ex & i2)
+{
+ if (!is_ex_of_type(i1, spinidx) || !is_ex_of_type(i2, spinidx))
+ throw(std::invalid_argument("indices of spinor metric must be of type spinidx"));
+ if (!ex_to_idx(i1).get_dim().is_equal(2) || !ex_to_idx(i2).get_dim().is_equal(2))
+ throw(std::runtime_error("index dimension for spinor metric must be 2"));
+
+ return indexed(spinmetric(), indexed::antisymmetric, i1, i2);
+}
+
ex epsilon_tensor(const ex & i1, const ex & i2)
{
if (!is_ex_of_type(i1, idx) || !is_ex_of_type(i2, idx))
git://www.ginac.de / ginac.git / blobdiff