#include "ncmul.h"
#include "numeric.h"
#include "power.h" // for sqrt()
+#include "symbol.h"
#include "print.h"
#include "archive.h"
#include "debugmsg.h"
/** Construct object without any color index. This constructor is for
* internal use only. Use the color_ONE() function instead.
* @see color_ONE */
-color::color(const ex & b, unsigned rl) : inherited(b), representation_label(rl)
+color::color(const ex & b, unsigned char rl) : inherited(b), representation_label(rl)
{
- debugmsg("color constructor from ex,unsigned", LOGLEVEL_CONSTRUCT);
+ debugmsg("color constructor from ex,unsigned char", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_color;
}
/** Construct object with one color index. This constructor is for internal
* use only. Use the color_T() function instead.
* @see color_T */
-color::color(const ex & b, const ex & i1, unsigned rl) : inherited(b, i1), representation_label(rl)
+color::color(const ex & b, const ex & i1, unsigned char rl) : inherited(b, i1), representation_label(rl)
{
- debugmsg("color constructor from ex,ex,unsigned", LOGLEVEL_CONSTRUCT);
+ debugmsg("color constructor from ex,ex,unsigned char", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_color;
}
-color::color(unsigned rl, const exvector & v, bool discardable) : inherited(indexed::unknown, v, discardable), representation_label(rl)
+color::color(unsigned char rl, const exvector & v, bool discardable) : inherited(indexed::unknown, v, discardable), representation_label(rl)
{
- debugmsg("color constructor from unsigned,exvector", LOGLEVEL_CONSTRUCT);
+ debugmsg("color constructor from unsigned char,exvector", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_color;
}
-color::color(unsigned rl, exvector * vp) : inherited(indexed::unknown, vp), representation_label(rl)
+color::color(unsigned char rl, exvector * vp) : inherited(indexed::unknown, vp), representation_label(rl)
{
- debugmsg("color constructor from unsigned,exvector *", LOGLEVEL_CONSTRUCT);
+ debugmsg("color constructor from unsigned char,exvector *", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_color;
}
color::color(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
{
debugmsg("color constructor from archive_node", LOGLEVEL_CONSTRUCT);
- n.find_unsigned("representation", representation_label);
+ unsigned rl;
+ n.find_unsigned("label", rl);
+ representation_label = rl;
}
void color::archive(archive_node &n) const
{
inherited::archive(n);
- n.add_unsigned("representation", representation_label);
+ n.add_unsigned("label", representation_label);
}
DEFAULT_UNARCHIVE(color)
// global functions
//////////
-ex color_ONE(unsigned rl)
+ex color_ONE(unsigned char rl)
{
return color(su3one(), rl);
}
-ex color_T(const ex & a, unsigned rl)
+ex color_T(const ex & a, unsigned char rl)
{
if (!is_ex_of_type(a, idx))
throw(std::invalid_argument("indices of color_T must be of type idx"));
return color_d(a, b, c) + I * color_f(a, b, c);
}
+/** Check whether a given tinfo key (as returned by return_type_tinfo()
+ * is that of a color object with the specified representation label. */
+static bool is_color_tinfo(unsigned ti, unsigned char rl)
+{
+ return ti == (TINFO_color + rl);
+}
+
+ex color_trace(const ex & e, unsigned char rl)
+{
+ if (is_ex_of_type(e, color)) {
+
+ if (ex_to_color(e).get_representation_label() == rl
+ && is_ex_of_type(e.op(0), su3one))
+ return _ex3();
+ else
+ return _ex0();
+
+ } else if (is_ex_exactly_of_type(e, add)) {
+
+ // Trace of sum = sum of traces
+ ex sum = _ex0();
+ for (unsigned i=0; i<e.nops(); i++)
+ sum += color_trace(e.op(i), rl);
+ return sum;
+
+ } else if (is_ex_exactly_of_type(e, mul)) {
+
+ // Trace of product: pull out non-color factors
+ ex prod = _ex1();
+ for (unsigned i=0; i<e.nops(); i++) {
+ const ex &o = e.op(i);
+ if (is_color_tinfo(o.return_type_tinfo(), rl))
+ prod *= color_trace(o, rl);
+ else
+ prod *= o;
+ }
+ return prod;
+
+ } else if (is_ex_exactly_of_type(e, ncmul)) {
+
+ if (!is_color_tinfo(e.return_type_tinfo(), rl))
+ return _ex0();
+
+ // Expand product, if necessary
+ ex e_expanded = e.expand();
+ if (!is_ex_of_type(e_expanded, ncmul))
+ return color_trace(e_expanded, rl);
+
+ unsigned num = e.nops();
+
+ if (num == 2) {
+
+ // Tr T_a T_b = 1/2 delta_a_b
+ return delta_tensor(e.op(0).op(1), e.op(1).op(1)) / 2;
+
+ } else if (num == 3) {
+
+ // Tr T_a T_b T_c = 1/4 h_a_b_c
+ return color_h(e.op(0).op(1), e.op(1).op(1), e.op(2).op(1)) / 4;
+
+ } else {
+
+ // Traces of 4 or more generators are computed recursively:
+ // Tr T_a1 .. T_an =
+ // 1/6 delta_a(n-1)_an Tr T_a1 .. T_a(n-2)
+ // + 1/2 h_a(n-1)_an_k Tr T_a1 .. T_a(n-2) T_k
+ const ex &last_index = e.op(num - 1).op(1);
+ const ex &next_to_last_index = e.op(num - 2).op(1);
+ idx summation_index((new symbol)->setflag(status_flags::dynallocated), 8);
+
+ exvector v1;
+ v1.reserve(num - 2);
+ for (int i=0; i<num-2; i++)
+ v1.push_back(e.op(i));
+
+ exvector v2 = v1;
+ v2.push_back(color_T(summation_index, rl));
+
+ return delta_tensor(next_to_last_index, last_index) * color_trace(ncmul(v1), rl) / 6
+ + color_h(next_to_last_index, last_index, summation_index) * color_trace(ncmul(v2), rl) / 2;
+ }
+ }
+
+ return _ex0();
+}
+
} // namespace GiNaC
git://www.ginac.de / ginac.git / blobdiff