// default constructors
//////////
-clifford::clifford() : representation_label(0), metric(lorentz_g(varidx((new symbol)->setflag(status_flags::dynallocated),4),varidx((new symbol)->setflag(status_flags::dynallocated),4)))
+static ex default_metric()
+{
+ static ex m = (new minkmetric)->setflag(status_flags::dynallocated);
+ return m;
+}
+
+clifford::clifford() : representation_label(0), metric(default_metric())
{
tinfo_key = TINFO_clifford;
}
/** Construct object without any indices. This constructor is for internal
* use only. Use the dirac_ONE() function instead.
* @see dirac_ONE */
- clifford::clifford(const ex & b, unsigned char rl) : inherited(b), representation_label(rl), metric(0)
+clifford::clifford(const ex & b, unsigned char rl) : inherited(b), representation_label(rl), metric(0)
{
tinfo_key = TINFO_clifford;
}
/** Construct object with one Lorentz index. This constructor is for internal
* use only. Use the clifford_unit() or dirac_gamma() functions instead.
- * @see clifford_unit
+ * @see clifford_unit
* @see dirac_gamma */
clifford::clifford(const ex & b, const ex & mu, const ex & metr, unsigned char rl) : inherited(b, mu), representation_label(rl), metric(metr)
{
tinfo_key = TINFO_clifford;
}
-clifford::clifford(unsigned char rl, const exvector & v, bool discardable, const ex & metr) : inherited(sy_none(), v, discardable), representation_label(rl), metric(metr)
+clifford::clifford(unsigned char rl, const ex & metr, const exvector & v, bool discardable) : inherited(not_symmetric(), v, discardable), representation_label(rl), metric(metr)
{
tinfo_key = TINFO_clifford;
}
-clifford::clifford(unsigned char rl, std::auto_ptr<exvector> vp, const ex & metr) : inherited(sy_none(), vp), representation_label(rl), metric(metr)
+clifford::clifford(unsigned char rl, const ex & metr, std::auto_ptr<exvector> vp) : inherited(not_symmetric(), vp), representation_label(rl), metric(metr)
{
tinfo_key = TINFO_clifford;
}
unsigned rl;
n.find_unsigned("label", rl);
representation_label = rl;
- ex m;
- n.find_ex("metric", m, sym_lst);
- metric = m;
+ n.find_ex("metric", metric, sym_lst);
}
void clifford::archive(archive_node &n) const
// functions overriding virtual functions from base classes
//////////
-ex clifford::get_metric(const ex & i, const ex & j) const
+ex clifford::get_metric(const ex & i, const ex & j) const
{
- return metric.subs(metric.op(1) == i).subs(metric.op(2) == j);
+ return indexed(metric, symmetric2(), i, j);
}
bool clifford::same_metric(const ex & other) const
{
if (is_a<clifford>(other)) {
- ex m = get_metric();
- return m.is_equal(ex_to<clifford>(other).get_metric(m.op(1), m.op(2)));
+ return get_metric().is_equal(ex_to<clifford>(other).get_metric());
} else if (is_a<indexed>(other)) {
- ex m = get_metric(other.op(1), other.op(2));
- return m.is_equal(other);
+ return get_metric(other.op(1), other.op(2)).is_equal(other);
} else
return false;
}
return false;
}
-/** An utility function looking for given metric within exvector,
- * used in cliffordunit::contract_with() */
-int find_same_metric(exvector & v, ex & c){
- for (int i=0; i<v.size();i++){
- if (!is_a<clifford>(v[i]) && is_a<indexed>(v[i])
+/** An utility function looking for a given metric within an exvector,
+ * used in cliffordunit::contract_with(). */
+static int find_same_metric(exvector & v, ex & c)
+{
+ for (int i=0; i<v.size();i++) {
+ if (!is_a<clifford>(v[i]) && is_a<indexed>(v[i])
&& ex_to<clifford>(c).same_metric(v[i])
&& (ex_to<varidx>(c.op(1)) == ex_to<indexed>(v[i]).get_indices()[0]
- || ex_to<varidx>(c.op(1)).toggle_variance() == ex_to<indexed>(v[i]).get_indices()[0])){
+ || ex_to<varidx>(c.op(1)).toggle_variance() == ex_to<indexed>(v[i]).get_indices()[0])) {
return ++i; // next to found
}
}
return 0; //nothing found
}
-/** Contraction of a Clifford units with something else. */
+/** Contraction of a Clifford unit with something else. */
bool cliffordunit::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
{
-
GINAC_ASSERT(is_a<clifford>(*self));
GINAC_ASSERT(is_a<indexed>(*other));
GINAC_ASSERT(is_a<cliffordunit>(self->op(0)));
if ((ex_to<clifford>(*other).get_representation_label() != rl)
&& unit.same_metric(*other))
return false;
+
// Find if a previous contraction produces the square of self
int prev_square = find_same_metric(v, self[0]);
- varidx d((new symbol)->setflag(status_flags::dynallocated), ex_to<idx>(ex_to<idx>(self->op(1)).get_dim()));
- ex squared_metric = unit.get_metric(self->op(1), d)*unit.get_metric(d.toggle_variance(), other->op(1));
+ varidx d((new symbol)->setflag(status_flags::dynallocated), ex_to<idx>(ex_to<idx>(self->op(1)).get_dim()));
+ ex squared_metric = unit.get_metric(self->op(1), d) * unit.get_metric(d.toggle_variance(), other->op(1));
// e~mu e.mu = Tr ONE
if (other - self == 1) {
const ex & ia = self[1].op(1);
const ex & ib = self[1].op(1);
- if (is_a<tensmetric>(unit.get_metric().op(0)))
+ if (is_a<tensmetric>(unit.get_metric()))
*self = 2 - unit.get_metric(self->op(1), other->op(1));
else if (prev_square != 0) {
- *self = 2-squared_metric;
+ *self = 2-squared_metric;
v[prev_square-1] = _ex1;
} else
*self = 2*unit.get_metric(ia, ib) - unit.get_metric(self->op(1), other->op(1));
const ex & ia = next_to_last->op(1);
const ex & ib = next_to_last->op(1);
- if (is_a<tensmetric>(unit.get_metric().op(0)))
+ if (is_a<tensmetric>(unit.get_metric()))
*self = 2 * (*next_to_last) * S - (*self) * S * (*other) * (*next_to_last);
else if (prev_square != 0) {
*self = 2 * (*next_to_last) * S - (*self) * S * (*other) * (*next_to_last)*unit.get_metric(self->op(1),self->op(1));
- v[prev_square-1] = _ex1;
+ v[prev_square-1] = _ex1;
} else
*self = 2 * (*next_to_last) * S* unit.get_metric(ia,ib) - (*self) * S * (*other) * (*next_to_last);
*next_to_last = _ex1;
const ex & ia = a.op(1);
const ex & ib = b.op(1);
if (ia.is_equal(ib)) { // gamma~alpha gamma~alpha -> g~alpha~alpha
- a = ex_to<clifford>(a).get_metric(ia,ib);
+ a = ex_to<clifford>(a).get_metric(ia, ib);
b = dirac_ONE(representation_label);
something_changed = true;
}
ex clifford::thiscontainer(const exvector & v) const
{
- return clifford(representation_label, v, false, get_metric());
+ return clifford(representation_label, get_metric(), v);
}
ex clifford::thiscontainer(std::auto_ptr<exvector> vp) const
{
- return clifford(representation_label, vp, get_metric());
+ return clifford(representation_label, get_metric(), vp);
}
ex diracgamma5::conjugate() const
ex dirac_ONE(unsigned char rl)
{
- return clifford(diracone(), rl);
+ static ex ONE = (new diracone)->setflag(status_flags::dynallocated);
+ return clifford(ONE, rl);
}
ex clifford_unit(const ex & mu, const ex & metr, unsigned char rl)
{
+ static ex unit = (new cliffordunit)->setflag(status_flags::dynallocated);
+
if (!is_a<varidx>(mu))
throw(std::invalid_argument("index of Clifford unit must be of type varidx"));
- if (!is_a<indexed>(metr))
- throw(std::invalid_argument("metric for Clifford unit must be of type indexed"));
- exvector d = ex_to<indexed>(metr).get_indices();
- if (d.size() > 2 || ex_to<idx>(d[0]).get_dim() != ex_to<idx>(d[1]).get_dim())
- //|| ex_to<idx>(d[0]).get_dim() != ex_to<idx>(mu).get_dim())
- throw(std::invalid_argument("metric is not square"));
- else
- ex_to<idx>(mu).replace_dim(ex_to<idx>(d[0]).get_dim());
- return clifford(cliffordunit(), mu, metr, rl);
+
+ return clifford(unit, mu, metr, rl);
}
ex dirac_gamma(const ex & mu, unsigned char rl)
{
+ static ex gamma = (new diracgamma)->setflag(status_flags::dynallocated);
+
if (!is_a<varidx>(mu))
throw(std::invalid_argument("index of Dirac gamma must be of type varidx"));
- ex dim = ex_to<idx>(mu).get_dim();
- return clifford(diracgamma(), mu, lorentz_g(varidx((new symbol)->setflag(status_flags::dynallocated), dim),varidx((new symbol)->setflag(status_flags::dynallocated), dim)), rl);
+ return clifford(gamma, mu, default_metric(), rl);
}
ex dirac_gamma5(unsigned char rl)
{
- return clifford(diracgamma5(), rl);
+ static ex gamma5 = (new diracgamma5)->setflag(status_flags::dynallocated);
+ return clifford(gamma5, rl);
}
ex dirac_gammaL(unsigned char rl)
{
- return clifford(diracgammaL(), rl);
+ static ex gammaL = (new diracgammaL)->setflag(status_flags::dynallocated);
+ return clifford(gammaL, rl);
}
ex dirac_gammaR(unsigned char rl)
{
- return clifford(diracgammaR(), rl);
+ static ex gammaR = (new diracgammaR)->setflag(status_flags::dynallocated);
+ return clifford(gammaR, rl);
}
ex dirac_slash(const ex & e, const ex & dim, unsigned char rl)
return aux.subs(srl, subs_options::no_pattern).simplify_indexed();
}
-ex clifford_prime (const ex &e) {
+ex clifford_prime(const ex &e)
+{
pointer_to_map_function fcn(clifford_prime);
if (is_a<clifford>(e) && is_a<cliffordunit>(e.op(0))) {
- return (-1)*e;
+ return -e;
} else if (is_a<add>(e)) {
return e.map(fcn);
} else if (is_a<ncmul>(e)) {
- return e.map(fcn);
+ return e.map(fcn);
} else if (is_a<power>(e)) {
- return pow(clifford_prime(e.op(0)),e.op(1));
- }
- else
+ return pow(clifford_prime(e.op(0)), e.op(1));
+ } else
return e;
-};
+}
-ex delete_ONE (const ex &e) {
+ex delete_ONE(const ex &e)
+{
pointer_to_map_function fcn(delete_ONE);
if (is_a<clifford>(e) && is_a<diracone>(e.op(0))) {
return 1;
} else if (is_a<add>(e)) {
return e.map(fcn);
} else if (is_a<ncmul>(e)) {
- return e.map(fcn);
+ return e.map(fcn);
} else if (is_a<mul>(e)) {
- return e.map(fcn);
+ return e.map(fcn);
} else if (is_a<power>(e)) {
- return pow(delete_ONE(e.op(0)),e.op(1));
- }
- else
+ return pow(delete_ONE(e.op(0)), e.op(1));
+ } else
return e;
-};
+}
-ex clifford_norm(const ex &e){
+ex clifford_norm(const ex &e)
+{
return sqrt(delete_ONE((e * clifford_bar(e)).simplify_indexed()));
-} ;
+}
-ex clifford_inverse(const ex &e) {
+ex clifford_inverse(const ex &e)
+{
ex norm = clifford_norm(e);
- if ( !norm.is_zero() )
- return clifford_bar(e)/pow(norm,2);
-};
+ if (!norm.is_zero())
+ return clifford_bar(e) / pow(norm, 2);
+}
-ex lst_to_clifford (const ex &v, const ex &mu, const ex &metr, unsigned char rl) {
+ex lst_to_clifford(const ex & v, const ex & mu, const ex & metr, unsigned char rl)
+{
unsigned min, max;
if (!ex_to<idx>(mu).is_dim_numeric())
throw(std::invalid_argument("Index should have a numeric dimension"));
unsigned dim = (ex_to<numeric>(ex_to<idx>(mu).get_dim())).to_int();
ex c = clifford_unit(mu, metr, rl);
- if (is_a<matrix>(v)) {
- if ( ex_to<matrix>(v).cols() > ex_to<matrix>(v).rows()){
+ if (is_a<matrix>(v)) {
+ if (ex_to<matrix>(v).cols() > ex_to<matrix>(v).rows()) {
min = ex_to<matrix>(v).rows();
max = ex_to<matrix>(v).cols();
} else {
min = ex_to<matrix>(v).cols();
max = ex_to<matrix>(v).rows();
}
- if (min == 1)
+ if (min == 1) {
if (dim == max)
if (is_a<varidx>(mu)) // need to swap variance
- return indexed(v,ex_to<varidx>(mu).toggle_variance())* c;
- else
- return indexed(v,mu)* c;
- else
+ return indexed(v, ex_to<varidx>(mu).toggle_variance()) * c;
+ else
+ return indexed(v, mu) * c;
+ else
throw(std::invalid_argument("Dimensions of vector and clifford unit mismatch"));
- else
+ } else
throw(std::invalid_argument("First argument should be a vector vector"));
- } else if (is_a<lst>(v))
+ } else if (is_a<lst>(v)) {
if (dim == ex_to<lst>(v).nops())
- return indexed(matrix(dim,1,ex_to<lst>(v)),ex_to<varidx>(mu).toggle_variance())* c;
+ return indexed(matrix(dim, 1, ex_to<lst>(v)), ex_to<varidx>(mu).toggle_variance()) * c;
else
throw(std::invalid_argument("List length and dimension of clifford unit mismatch"));
- else
+ } else
throw(std::invalid_argument("Cannot construct from anything but list or vector"));
-};
+}
-
- } // namespace GiNaC
-
+} // namespace GiNaC
git://www.ginac.de / ginac.git / blobdiff