}
}
+/** Predicate for finding non-clifford objects. */
+struct is_not_a_clifford : public std::unary_function<ex, bool> {
+ bool operator()(const ex & e)
+ {
+ return !is_a<clifford>(e);
+ }
+};
+
/** Contraction of a gamma matrix with something else. */
bool diracgamma::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
{
if (ex_to<clifford>(*other).get_representation_label() != rl)
return false;
+ size_t num = other - self;
+
// gamma~mu gamma.mu = dim ONE
- if (other - self == 1) {
+ if (num == 1) {
*self = dim;
*other = dirac_ONE(rl);
return true;
// gamma~mu gamma~alpha gamma.mu = (2-dim) gamma~alpha
- } else if (other - self == 2
+ } else if (num == 2
&& is_a<clifford>(self[1])) {
*self = 2 - dim;
*other = _ex1;
return true;
// gamma~mu gamma~alpha gamma~beta gamma.mu = 4 g~alpha~beta + (dim-4) gamam~alpha gamma~beta
- } else if (other - self == 3
+ } else if (num == 3
&& is_a<clifford>(self[1])
&& is_a<clifford>(self[2])) {
ex b1, i1, b2, i2;
return true;
// gamma~mu gamma~alpha gamma~beta gamma~delta gamma.mu = -2 gamma~delta gamma~beta gamma~alpha - (dim-4) gamam~alpha gamma~beta gamma~delta
- } else if (other - self == 4
+ } else if (num == 4
&& is_a<clifford>(self[1])
&& is_a<clifford>(self[2])
&& is_a<clifford>(self[3])) {
*other = _ex1;
return true;
+ // gamma~mu Sodd gamma.mu = -2 Sodd_R
+ // (Chisholm identity in 4 dimensions)
+ } else if (!((other - self) & 1) && dim.is_equal(4)) {
+ if (std::find_if(self + 1, other, is_not_a_clifford()) != other)
+ return false;
+
+ *self = ncmul(exvector(std::reverse_iterator<exvector::const_iterator>(other), std::reverse_iterator<exvector::const_iterator>(self + 1)), true);
+ std::fill(self + 1, other, _ex1);
+ *other = _ex_2;
+ return true;
+
+ // gamma~mu Sodd gamma~alpha gamma.mu = 2 gamma~alpha Sodd + 2 Sodd_R gamma~alpha
+ // (commutate contracted indices towards each other, then use
+ // Chisholm identity in 4 dimensions)
+ } else if (((other - self) & 1) && dim.is_equal(4)) {
+ if (std::find_if(self + 1, other, is_not_a_clifford()) != other)
+ return false;
+
+ exvector::iterator next_to_last = other - 1;
+ ex S = ncmul(exvector(self + 1, next_to_last), true);
+ ex SR = ncmul(exvector(std::reverse_iterator<exvector::const_iterator>(next_to_last), std::reverse_iterator<exvector::const_iterator>(self + 1)), true);
+
+ *self = (*next_to_last) * S + SR * (*next_to_last);
+ std::fill(self + 1, other, _ex1);
+ *other = _ex2;
+ return true;
+
// gamma~mu S gamma~alpha gamma.mu = 2 gamma~alpha S - gamma~mu S gamma.mu gamma~alpha
// (commutate contracted indices towards each other, simplify_indexed()
// will re-expand and re-run the simplification)
} else {
- exvector::iterator it = self + 1, next_to_last = other - 1;
- while (it != other) {
- if (!is_a<clifford>(*it))
- return false;
- ++it;
- }
+ if (std::find_if(self + 1, other, is_not_a_clifford()) != other)
+ return false;
- it = self + 1;
- ex S = _ex1;
- while (it != next_to_last) {
- S *= *it;
- *it++ = _ex1;
- }
+ exvector::iterator next_to_last = other - 1;
+ ex S = ncmul(exvector(self + 1, next_to_last), true);
*self = 2 * (*next_to_last) * S - (*self) * S * (*other) * (*next_to_last);
- *next_to_last = _ex1;
- *other = _ex1;
+ std::fill(self + 1, other + 1, _ex1);
return true;
}
bool something_changed = false;
int sign = 1;
- // Anticommute gamma5/L/R's to the front
+ // Anticommutate gamma5/L/R's to the front
if (s.size() >= 2) {
exvector::iterator first = s.begin(), next_to_last = s.end() - 2;
while (true) {
// Slashed vectors are actually stored as a clifford object with the
// vector as its base expression and a (dummy) index that just serves
// for storing the space dimensionality
- return clifford(e, varidx(0, dim), rl);
+ return clifford(e, varidx(0, dim), default_metric(), rl);
}
/** Check whether a given tinfo key (as returned by return_type_tinfo()
return (ti & ~0xff) == TINFO_clifford;
}
+/** Extract representation label from tinfo key (as returned by
+ * return_type_tinfo()). */
+static unsigned char get_representation_label(unsigned ti)
+{
+ return ti & 0xff;
+}
+
/** Take trace of a string of an even number of Dirac gammas given a vector
* of indices. */
static ex trace_string(exvector::const_iterator ix, size_t num)
return result;
}
-ex dirac_trace(const ex & e, unsigned char rl, const ex & trONE)
+ex dirac_trace(const ex & e, const std::set<unsigned char> & rls, const ex & trONE)
{
if (is_a<clifford>(e)) {
- if (!ex_to<clifford>(e).get_representation_label() == rl)
- return _ex0;
+ unsigned char rl = ex_to<clifford>(e).get_representation_label();
+
+ // Are we taking the trace over this object's representation label?
+ if (rls.find(rl) == rls.end())
+ return e;
+
+ // Yes, all elements are traceless, except for dirac_ONE and dirac_L/R
const ex & g = e.op(0);
if (is_a<diracone>(g))
return trONE;
ex prod = _ex1;
for (size_t i=0; i<e.nops(); i++) {
const ex &o = e.op(i);
- if (is_clifford_tinfo(o.return_type_tinfo(), rl))
- prod *= dirac_trace(o, rl, trONE);
+ if (is_clifford_tinfo(o.return_type_tinfo()))
+ prod *= dirac_trace(o, rls, trONE);
else
prod *= o;
}
} else if (is_exactly_a<ncmul>(e)) {
- if (!is_clifford_tinfo(e.return_type_tinfo(), rl))
- return _ex0;
+ unsigned char rl = get_representation_label(e.return_type_tinfo());
+
+ // Are we taking the trace over this string's representation label?
+ if (rls.find(rl) == rls.end())
+ return e;
// Substitute gammaL/R and expand product, if necessary
ex e_expanded = e.subs(lst(
dirac_gammaR(rl) == (dirac_ONE(rl)+dirac_gamma5(rl))/2
), subs_options::no_pattern).expand();
if (!is_a<ncmul>(e_expanded))
- return dirac_trace(e_expanded, rl, trONE);
+ return dirac_trace(e_expanded, rls, trONE);
// gamma5 gets moved to the front so this check is enough
bool has_gamma5 = is_a<diracgamma5>(e.op(0).op(0));
} else if (e.nops() > 0) {
// Trace maps to all other container classes (this includes sums)
- pointer_to_map_function_2args<unsigned char, const ex &> fcn(dirac_trace, rl, trONE);
+ pointer_to_map_function_2args<const std::set<unsigned char> &, const ex &> fcn(dirac_trace, rls, trONE);
return e.map(fcn);
} else
return _ex0;
}
+ex dirac_trace(const ex & e, const lst & rll, const ex & trONE)
+{
+ // Convert list to set
+ std::set<unsigned char> rls;
+ for (lst::const_iterator i = rll.begin(); i != rll.end(); ++i) {
+ if (i->info(info_flags::nonnegint))
+ rls.insert(ex_to<numeric>(*i).to_int());
+ }
+
+ return dirac_trace(e, rls, trONE);
+}
+
+ex dirac_trace(const ex & e, unsigned char rl, const ex & trONE)
+{
+ // Convert label to set
+ std::set<unsigned char> rls;
+ rls.insert(rl);
+
+ return dirac_trace(e, rls, trONE);
+}
+
+
ex canonicalize_clifford(const ex & e)
{
// Scan for any ncmul objects
git://www.ginac.de / ginac.git / blobdiff