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#include "Cleanup.hh"
#include "Exceptions.hh"
#include "algorithms/fierz.hh"
#include "properties/GammaMatrix.hh"
#include "properties/Integer.hh"
#include "properties/DiracBar.hh"
using namespace cadabra;
// #define DEBUG(ln) ln
#define DEBUG(ln)
fierz::fierz(const Kernel& k, Ex& e, Ex& args)
: Algorithm(k, e), spinor_list(Ex(args.begin()))
{
if(*(spinor_list.begin()->name)!="\\comma")
throw ArgumentException("fierz: need a list of spinors");
if(tr.number_of_children(spinor_list.begin())!=4)
throw ArgumentException("fierz: need a list of 4 spinors.");
}
bool fierz::can_apply(iterator it)
{
if(*it->name!="\\prod") return false;
// Find a Dirac bar, and then continue inside the product
// to find the gamma matrix, fermion and second fermi bilinear.
sibling_iterator sib=tr.begin(it);
const Integer *indit=0;
while(sib!=tr.end(it)) {
const DiracBar *db=kernel.properties.get<DiracBar>(sib);
if(db) {
DEBUG( std::cerr << "found db" << sib << std::endl; );
spin1=sib;
prop1=kernel.properties.get<Spinor>(spin1);
sibling_iterator ch=sib;
const GammaMatrix *gmnxt=0;
const Spinor *spnxt=0;
// Skip to next spinor-index carrying object
do {
++ch;
if(ch==tr.end(it)) break;
gmnxt=kernel.properties.get<GammaMatrix>(ch);
spnxt=kernel.properties.get<Spinor>(ch);
}
while(gmnxt==0 && spnxt==0);
if(gmnxt) {
DEBUG( std::cerr << "found gamma " << ch << std::endl; );
// FIXME: should also work when there is a unit matrix in between.
indit=kernel.properties.get<Integer>(ch.begin(), true);
indprop=kernel.properties.get<Indices>(ch.begin(), true);
if(!indit || !indprop) return false;
dim=to_long(*indit->difference.begin()->multiplier);
if(dim==1)
return false;
gam1=ch;
// Skip to next spinor-index carrying object
do {
++ch;
if(ch==tr.end(it)) break;
spnxt=kernel.properties.get<Spinor>(ch);
gmnxt=kernel.properties.get<GammaMatrix>(ch);
}
while(gmnxt==0 && spnxt==0);
prop2=spnxt;
if(prop2) { // one fermi bilinear found.
DEBUG( std::cerr << "found spin2 " << Ex(ch) << std::endl; );
spin2=ch;
// Skip to next spinor-index carrying object
do {
++ch;
if(ch==tr.end(it)) break;
spnxt=kernel.properties.get<Spinor>(ch);
gmnxt=kernel.properties.get<GammaMatrix>(ch);
}
while(gmnxt==0 && spnxt==0);
db=kernel.properties.get<DiracBar>(ch);
if(db) {
DEBUG( std::cerr << "found db2" << std::endl; );
spin3=ch;
prop3=spnxt;
// Skip to next spinor-index carrying object
do {
++ch;
if(ch==tr.end(it)) break;
spnxt=kernel.properties.get<Spinor>(ch);
gmnxt=kernel.properties.get<GammaMatrix>(ch);
}
while(gmnxt==0 && spnxt==0);
if(gmnxt) {
gam2=ch;
DEBUG( std::cerr << "found gam2: " << gam2 << std::endl; );
// Skip to next spinor-index carrying object
do {
++ch;
if(ch==tr.end(it)) break;
spnxt=kernel.properties.get<Spinor>(ch);
gmnxt=kernel.properties.get<GammaMatrix>(ch);
}
while(gmnxt==0 && spnxt==0);
prop4=spnxt;
if(prop4) {
DEBUG( std::cerr << "found spin4" << std::endl; );
spin4=ch;
return true;
}
}
}
}
}
}
++sib;
}
return false;
}
Algorithm::result_t fierz::apply(iterator& it)
{
sibling_iterator spt=spinor_list.begin(spinor_list.begin());
// Catch terms with spinors in the right order.
if(subtree_equal(&kernel.properties, tr.begin(spin1), spt)) {
++spt;
if(subtree_equal(&kernel.properties, spin2, spt)) {
++spt;
if(subtree_equal(&kernel.properties, tr.begin(spin3), spt)) {
++spt;
if(subtree_equal(&kernel.properties, spin4, spt)) {
DEBUG( std::cerr << "Found term with spinors in correct order already" << std::endl; );
return result_t::l_no_action;
}
}
}
}
// Catch terms with right spinors but wrong order.
bool doit=false;
spt=spinor_list.begin(spinor_list.begin());
if(subtree_equal(&kernel.properties, tr.begin(spin1), spt)) {
++spt;
if(subtree_equal(&kernel.properties, spin4, spt)) {
++spt;
if(subtree_equal(&kernel.properties, tr.begin(spin3), spt)) {
++spt;
if(subtree_equal(&kernel.properties, spin2, spt)) {
DEBUG( std::cerr << "Found term with spinors wrong order" << std::endl; );
doit=true;
}
}
}
}
if(!doit) {
DEBUG( std::cerr << "Spinors in this factor do not match algorithm list." << std::endl; );
return result_t::l_no_action;
}
// txtout << "going to Fierz" << std::endl;
Ex rep("\\sum");
index_map_t ind_free, ind_dummy;
classify_indices(it, ind_free, ind_dummy);
spinordim=(1 << dim/2);
int maxind=dim;
if(prop1->weyl || dim%2==1)
maxind/=2;
for(int i=0; i<=maxind; ++i) {
DEBUG( std::cerr << i << " of " << maxind << std::endl; );
// Make a copy of this term, moving the gamma matrices into the
// first factor and inserting projector gamma matrices as well.
Ex cpyterm("\\prod");
cpyterm.begin()->multiplier=it->multiplier;
multiply(cpyterm.begin()->multiplier, multiplier_t(-1)/multiplier_t(spinordim));
if(i>0)
multiply(cpyterm.begin()->multiplier, multiplier_t(1)/multiplier_t(combin::fact<int>(i)));
sibling_iterator cpit=tr.begin(it);
// Copy and put the gammas and projector gammas in the right spot.
iterator locgam1, locgam2; // locations of the projector gammas
while(cpit!=tr.end(it)) {
iterator tmpit;
if(cpit==spin2)
tmpit=cpyterm.append_child(cpyterm.begin(), spin4);
else if(cpit==spin4)
tmpit=cpyterm.append_child(cpyterm.begin(), spin2);
else tmpit=cpyterm.append_child(cpyterm.begin(), (iterator)cpit);
if(cpit==gam1) {
if(i>0) {
locgam1=cpyterm.append_child(cpyterm.begin(), gam1);
cpyterm.erase_children(locgam1);
}
cpyterm.append_child(cpyterm.begin(), gam2);
}
if(cpit==gam2) {
locgam2=tmpit;
if(i==0) cpyterm.erase(locgam2);
else cpyterm.erase_children(locgam2);
if(i>0)
DEBUG( std::cerr << "New gamma reads " << Ex(locgam2) << std::endl; );
}
++cpit;
}
// Insert the indices on the projector gammas.
index_map_t ind_added;
for(int j=1; j<=i; ++j) {
Ex newdum=get_dummy(indprop, &ind_free, &ind_dummy, &ind_added);
iterator loc1=cpyterm.append_child(locgam1, newdum.begin());
ind_added.insert(index_map_t::value_type(newdum, loc1));
loc1->fl.parent_rel=str_node::p_super;
// Add the indices in opposite order in the second gamma matrix
// std::cerr << "inserting " << newdum << " at " << Ex(locgam2) << std::endl;
iterator loc2=cpyterm.prepend_child(locgam2, newdum.begin());
if(indprop->position_type==Indices::free)
loc1->fl.parent_rel=str_node::p_super;
else
loc2->fl.parent_rel=str_node::p_sub;
}
// std::cerr << cpyterm << std::endl;
rep.append_child(rep.begin(), cpyterm.begin());
}
// std::cerr << rep << std::endl;
it=tr.replace(it, rep.begin());
cleanup_dispatch(kernel, tr, it);
return result_t::l_applied;
}
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