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/*
Cadabra: a field-theory motivated computer algebra system.
Copyright (C) 2001-2011 Kasper Peeters <kasper.peeters@aei.mpg.de>
This program is free software: you can redistribute it and/or
modify it under the terms of the GNU General Public License as
published by the Free Software Foundation, either version 3 of the
License, or (at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
#include <map>
#include "Exchange.hh"
#include "Compare.hh"
#include "Algorithm.hh"
#include "properties/DiracBar.hh"
using namespace cadabra;
// Find groups of identical tensors.
//
int exchange::collect_identical_tensors(const Properties& properties, Ex& tr, Ex::iterator it,
std::vector<identical_tensors_t>& idts)
{
assert(*it->name=="\\prod");
int total_number_of_indices=0; // refers to number of indices on gamma matrices
Ex::sibling_iterator sib=it.begin();
while(sib!=it.end()) {
unsigned int i=0;
if(Algorithm::number_of_indices(properties, sib)==0) {
++sib;
continue;
}
if(properties.get<GammaMatrix>(sib)) {
total_number_of_indices+=Algorithm::number_of_indices(properties, sib);
++sib;
continue;
}
// In case of spinors, the name may be hidden inside a Dirac bar.
Ex::sibling_iterator truetensor=sib;
const DiracBar *db=properties.get<DiracBar>(truetensor);
if(db)
truetensor=tr.begin(truetensor);
Ex_comparator comp(properties);
// Compare the current tensor with all other tensors encountered so far.
for(; i<idts.size(); ++i) {
Ex::sibling_iterator truetensor2=idts[i].tensors[0];
const DiracBar *db2=properties.get<DiracBar>(truetensor2);
if(db2)
truetensor2=tr.begin(truetensor2);
comp.clear();
auto match = comp.equal_subtree(truetensor2, truetensor);
if(match==Ex_comparator::match_t::subtree_match ||
match==Ex_comparator::match_t::match_index_less ||
match==Ex_comparator::match_t::match_index_greater) {
// If this is a spinor, check that it's connected to the one already stored
// by a Gamma matrix, or that it is connected directly.
if(idts[i].spino) {
Ex::sibling_iterator tmpit=idts[i].tensors[0];
const GammaMatrix *gmnxt=0;
const Spinor *spnxt=0;
// skip objects without spinor line
do {
++tmpit;
gmnxt=properties.get<GammaMatrix>(tmpit);
spnxt=properties.get<Spinor>(tmpit);
}
while(gmnxt==0 && spnxt==0);
if(tmpit==sib) {
// txtout << "using fermi exchange" << std::endl;
idts[i].extra_sign++;
break;
}
if(gmnxt) {
// txtout << "gamma next " << std::endl;
int numind=Algorithm::number_of_indices(properties, tmpit);
// skip objects without spinor line
do {
++tmpit;
gmnxt=properties.get<GammaMatrix>(tmpit);
spnxt=properties.get<Spinor>(tmpit);
}
while(gmnxt==0 && spnxt==0);
if(tmpit==sib) { // yes, it's a proper Majorana spinor pair.
// txtout << "using fermi exchange with gamma " << numind << std::endl;
if( ((numind*(numind+1))/2)%2 == 0 )
idts[i].extra_sign++;
break;
}
}
}
else break;
}
}
if(i==idts.size()) {
identical_tensors_t ngr;
ngr.comm=properties.get<SelfCommutingBehaviour>(sib, true);
// if(ngr.comm)
// std::cerr << "selfcomm " << ngr.comm->sign() << " for " << sib << std::endl;
ngr.spino=properties.get<Spinor>(sib);
ngr.tab=properties.get<TableauBase>(sib);
ngr.traceless=properties.get<Traceless>(sib);
ngr.gammatraceless=properties.get<GammaTraceless>(sib);
ngr.extra_sign=0;
ngr.number_of_indices=Algorithm::number_of_indices(properties, truetensor);
ngr.tensors.push_back(sib);
ngr.seq_numbers_of_first_indices.push_back(total_number_of_indices);
total_number_of_indices+=ngr.number_of_indices;
if(ngr.spino==0 || ngr.spino->majorana==true)
idts.push_back(ngr);
}
else {
idts[i].tensors.push_back(sib);
idts[i].seq_numbers_of_first_indices.push_back(total_number_of_indices);
total_number_of_indices+=idts[i].number_of_indices;
}
++sib;
}
return total_number_of_indices;
}
bool exchange::get_node_gs(const Properties& properties, Ex& tr, Ex::iterator it, std::vector<std::vector<int> >& gs)
{
std::vector<identical_tensors_t> idts;
int total_number_of_indices=collect_identical_tensors(properties, tr, it, idts);
if(idts.size()==0) return true; // no indices, so nothing to permute
// Make a strong generating set for the permutation of identical tensors.
for(unsigned int i=0; i<idts.size(); ++i) {
unsigned int num=idts[i].tensors.size();
if(idts[i].comm)
if(idts[i].comm->sign()==0) continue;
if(num>1) {
std::vector<int> gsel(total_number_of_indices+2);
for(unsigned int sobj=0; sobj<num-1; ++sobj) {
for(int kk=0; kk<total_number_of_indices+2; ++kk)
gsel[kk]=kk+1;
// permutation of sobj & obj for all sobj and obj > sobj.
for(unsigned int obj=sobj; obj<num-1; ++obj) {
for(unsigned int kk=0; kk<idts[i].number_of_indices; ++kk)
std::swap(gsel[idts[i].seq_numbers_of_first_indices[obj]+kk],
gsel[idts[i].seq_numbers_of_first_indices[obj+1]+kk]);
if(idts[i].spino) {
assert(num==2); // FIXME: cannot yet do more than two fermions
if(idts[i].extra_sign%2==1) {
std::swap(gsel[total_number_of_indices], gsel[total_number_of_indices+1]);
}
}
if(idts[i].comm) {
if(idts[i].comm->sign()==-1)
std::swap(gsel[total_number_of_indices], gsel[total_number_of_indices+1]);
}
if(idts[i].spino && idts[i].number_of_indices==0) {
if(gsel[total_number_of_indices+1]==total_number_of_indices+1)
return false;
}
else gs.push_back(gsel);
}
}
}
}
// for(unsigned int i=0; i<idts.size(); ++i) {
// int num=idts[i].tensors.size();
// if(num>1) {
// for(int t1=0; t1<num-1; ++t1) {
// for(int t2=t1+1; t2<num; ++t2) {
// std::vector<int> gsel(total_number_of_indices+2);
// for(int kk=0; kk<total_number_of_indices+2; ++kk)
// gsel[kk]=kk+1;
//
// if(idts[i].spino) {
// assert(num==2); // FIXME: cannot yet do more than two fermions
// if(idts[i].extra_sign%2==1) {
// // txtout << "extra sign" << std::endl;
// std::swap(gsel[total_number_of_indices], gsel[total_number_of_indices+1]);
// }
// }
// for(unsigned int kk=0; kk<idts[i].number_of_indices; ++kk)
// std::swap(gsel[idts[i].seq_numbers_of_first_indices[t1]+kk],
// gsel[idts[i].seq_numbers_of_first_indices[t2]+kk]);
// // for(int kk=0; kk<total_number_of_indices+2; ++kk) {
// // txtout << gsel[kk] << " ";
// // }
// // txtout << std::endl;
// // txtout << "adding gs element" << std::endl;
//
// if(idts[i].comm) {
// if(idts[i].comm->sign()==-1) {
// // txtout << "anticommuting" << std::endl;
// std::swap(gsel[total_number_of_indices], gsel[total_number_of_indices+1]);
// }
// else if(idts[i].comm->sign()==0)
// return false;
// }
//
// if(idts[i].spino && idts[i].number_of_indices==0) {
// if(gsel[total_number_of_indices+1]==total_number_of_indices+1)
// return false;
// }
// else gs.push_back(gsel);
// }
// }
// }
// }
return true;
}
bool operator<(const exchange::tensor_type_t& one, const exchange::tensor_type_t& two)
{
if(*one.name < *two.name) return true;
if(one.name == two.name)
if(one.number_of_indices < two.number_of_indices) return true;
return false;
}
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