color.cpp

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/*
 *  GiNaC Copyright (C) 1999-2023 Johannes Gutenberg University Mainz, Germany
 *
 *  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 2 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, write to the Free Software
 *  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
 */
 
#include "color.h"
#include "idx.h"
#include "ncmul.h"
#include "symmetry.h"
#include "operators.h"
#include "numeric.h"
#include "mul.h"
#include "power.h" // for sqrt()
#include "symbol.h"
#include "archive.h"
#include "utils.h"
 
#include <iostream>
#include <stdexcept>
 
namespace GiNaC {
 
GINAC_IMPLEMENT_REGISTERED_CLASS(color, indexed)
 
GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(su3one, tensor,
  print_func<print_dflt>(&su3one::do_print).
  print_func<print_latex>(&su3one::do_print_latex))
 
GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(su3t, tensor,
  print_func<print_dflt>(&su3t::do_print).
  print_func<print_latex>(&su3t::do_print))
 
GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(su3f, tensor,
  print_func<print_dflt>(&su3f::do_print).
  print_func<print_latex>(&su3f::do_print))
 
GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(su3d, tensor,
  print_func<print_dflt>(&su3d::do_print).
  print_func<print_latex>(&su3d::do_print))
 
// default constructors
 
color::color() : representation_label(0)
{
}
 
DEFAULT_CTOR(su3one)
DEFAULT_CTOR(su3t)
DEFAULT_CTOR(su3f)
DEFAULT_CTOR(su3d)
 
 
// other constructors
 
color::color(const ex & b, unsigned char rl) : inherited(b), representation_label(rl)
{
}
 
color::color(const ex & b, const ex & i1, unsigned char rl) : inherited(b, i1), representation_label(rl)
{
}
 
color::color(unsigned char rl, const exvector & v) : inherited(not_symmetric(), v), representation_label(rl)
{
}
 
color::color(unsigned char rl, exvector && v) : inherited(not_symmetric(), std::move(v)), representation_label(rl)
{
}
 
return_type_t color::return_type_tinfo() const
{
    return make_return_type_t<color>(representation_label);
}
 
// archiving
 
void color::read_archive(const archive_node& n, lst& sym_lst)
{
    inherited::read_archive(n, sym_lst);
    unsigned rl;
    n.find_unsigned("label", rl);
    representation_label = rl;
}
 
void color::archive(archive_node &n) const
{
    inherited::archive(n);
    n.add_unsigned("label", representation_label);
}
 
GINAC_BIND_UNARCHIVER(color);
GINAC_BIND_UNARCHIVER(su3one);
GINAC_BIND_UNARCHIVER(su3t);
GINAC_BIND_UNARCHIVER(su3f);
GINAC_BIND_UNARCHIVER(su3d);
 
// functions overriding virtual functions from base classes
 
int color::compare_same_type(const basic & other) const
{
    GINAC_ASSERT(is_a<color>(other));
    const color &o = static_cast<const color &>(other);
 
    if (representation_label != o.representation_label) {
        // different representation label
        return representation_label < o.representation_label ? -1 : 1;
    }
 
    return inherited::compare_same_type(other);
}
 
bool color::match_same_type(const basic & other) const
{
    GINAC_ASSERT(is_a<color>(other));
    const color &o = static_cast<const color &>(other);
 
    return representation_label == o.representation_label;
}
 
DEFAULT_COMPARE(su3one)
DEFAULT_COMPARE(su3t)
DEFAULT_COMPARE(su3f)
DEFAULT_COMPARE(su3d)
 
DEFAULT_PRINT_LATEX(su3one, "ONE", "\\mathbb{1}")
DEFAULT_PRINT(su3t, "T")
DEFAULT_PRINT(su3f, "f")
DEFAULT_PRINT(su3d, "d")
 
ex color::eval_ncmul(const exvector & v) const
{
    exvector s;
    s.reserve(v.size());
 
    // Remove superfluous ONEs
    for (auto & it : v) {
        if (!is_a<su3one>(it.op(0)))
            s.push_back(it);
    }
 
    if (s.empty())
        return color(su3one(), representation_label);
    else
        return hold_ncmul(s);
}
 
ex color::thiscontainer(const exvector & v) const
{
    return color(representation_label, v);
}
 
ex color::thiscontainer(exvector && v) const
{
    return color(representation_label, std::move(v));
}
 
static ex permute_free_index_to_front(const exvector & iv3, const exvector & iv2, int & sig)
{
    GINAC_ASSERT(iv3.size() == 3);
    GINAC_ASSERT(iv2.size() == 2);
 
    sig = 1;
 
#define TEST_PERMUTATION(A,B,C,P) \
    if (iv3[B].is_equal(iv2[0]) && iv3[C].is_equal(iv2[1])) { \
        sig = P; \
        return iv3[A]; \
    }
    
    TEST_PERMUTATION(0,1,2,  1);
    TEST_PERMUTATION(0,2,1, -1);
    TEST_PERMUTATION(1,0,2, -1);
    TEST_PERMUTATION(1,2,0,  1);
    TEST_PERMUTATION(2,0,1,  1);
    TEST_PERMUTATION(2,1,0, -1);
 
    throw(std::logic_error("permute_free_index_to_front(): no valid permutation found"));
}
 
ex su3d::eval_indexed(const basic & i) const
{
    GINAC_ASSERT(is_a<indexed>(i));
    GINAC_ASSERT(i.nops() == 4);
    GINAC_ASSERT(is_a<su3d>(i.op(0)));
 
    // Convolutions are zero
    if (!(static_cast<const indexed &>(i).get_dummy_indices().empty()))
        return _ex0;
 
    // Numeric evaluation
    if (static_cast<const indexed &>(i).all_index_values_are(info_flags::nonnegint)) {
 
        // Sort indices
        int v[3];
        for (unsigned j=0; j<3; j++)
            v[j] = ex_to<numeric>(ex_to<idx>(i.op(j + 1)).get_value()).to_int();
        if (v[0] > v[1]) std::swap(v[0], v[1]);
        if (v[0] > v[2]) std::swap(v[0], v[2]);
        if (v[1] > v[2]) std::swap(v[1], v[2]);
 
#define CMPINDICES(A,B,C) ((v[0] == (A)) && (v[1] == (B)) && (v[2] == (C)))
 
        // Check for non-zero elements
        if (CMPINDICES(1,4,6) || CMPINDICES(1,5,7) || CMPINDICES(2,5,6)
         || CMPINDICES(3,4,4) || CMPINDICES(3,5,5))
            return _ex1_2;
        else if (CMPINDICES(2,4,7) || CMPINDICES(3,6,6) || CMPINDICES(3,7,7))
            return _ex_1_2;
        else if (CMPINDICES(1,1,8) || CMPINDICES(2,2,8) || CMPINDICES(3,3,8))
            return sqrt(_ex3)*_ex1_3;
        else if (CMPINDICES(8,8,8))
            return sqrt(_ex3)*_ex_1_3;
        else if (CMPINDICES(4,4,8) || CMPINDICES(5,5,8)
              || CMPINDICES(6,6,8) || CMPINDICES(7,7,8))
            return sqrt(_ex3)/_ex_6;
        else
            return _ex0;
    }
 
    // No further simplifications
    return i.hold();
}
 
ex su3f::eval_indexed(const basic & i) const
{
    GINAC_ASSERT(is_a<indexed>(i));
    GINAC_ASSERT(i.nops() == 4);
    GINAC_ASSERT(is_a<su3f>(i.op(0)));
 
    // Numeric evaluation
    if (static_cast<const indexed &>(i).all_index_values_are(info_flags::nonnegint)) {
 
        // Sort indices, remember permutation sign
        int v[3];
        for (unsigned j=0; j<3; j++)
            v[j] = ex_to<numeric>(ex_to<idx>(i.op(j + 1)).get_value()).to_int();
        int sign = 1;
        if (v[0] > v[1]) { std::swap(v[0], v[1]); sign = -sign; }
        if (v[0] > v[2]) { std::swap(v[0], v[2]); sign = -sign; }
        if (v[1] > v[2]) { std::swap(v[1], v[2]); sign = -sign; }
 
        // Check for non-zero elements
        if (CMPINDICES(1,2,3))
            return sign;
        else if (CMPINDICES(1,4,7) || CMPINDICES(2,4,6)
              || CMPINDICES(2,5,7) || CMPINDICES(3,4,5))
            return _ex1_2 * sign;
        else if (CMPINDICES(1,5,6) || CMPINDICES(3,6,7))
            return _ex_1_2 * sign;
        else if (CMPINDICES(4,5,8) || CMPINDICES(6,7,8))
            return sqrt(_ex3)/2 * sign;
        else
            return _ex0;
    }
 
    // No further simplifications
    return i.hold();
}
 
 
bool su3t::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
{
    GINAC_ASSERT(is_a<indexed>(*self));
    GINAC_ASSERT(is_a<indexed>(*other));
    GINAC_ASSERT(self->nops() == 2);
    GINAC_ASSERT(is_a<su3t>(self->op(0)));
    unsigned char rl = ex_to<color>(*self).get_representation_label();
 
    if (is_exactly_a<su3t>(other->op(0))) {
 
        // Contraction only makes sense if the representation labels are equal
        GINAC_ASSERT(is_a<color>(*other));
        if (ex_to<color>(*other).get_representation_label() != rl)
            return false;
 
        // T.a T.a = 4/3 ONE
        if (other - self == 1) {
            *self = numeric(4, 3);
            *other = color_ONE(rl);
            return true;
 
        // T.a T.b T.a = -1/6 T.b
        } else if (other - self == 2
                && is_a<color>(self[1])) {
            *self = numeric(-1, 6);
            *other = _ex1;
            return true;
 
        // T.a S T.a = 1/2 Tr(S) - 1/6 S
        } else {
            auto it = self + 1;
            while (it != other) {
                if (!is_a<color>(*it)) {
                    return false;
                }
                it++;
            }
 
            it = self + 1;
            ex S = _ex1;
            while (it != other) {
                S *= *it;
                *it++ = _ex1;
            }
 
            *self = color_trace(S, rl) * color_ONE(rl) / 2 - S / 6;
            *other = _ex1;
            return true;
        }
    }
 
    return false;
}
 
bool su3d::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
{
    GINAC_ASSERT(is_a<indexed>(*self));
    GINAC_ASSERT(is_a<indexed>(*other));
    GINAC_ASSERT(self->nops() == 4);
    GINAC_ASSERT(is_a<su3d>(self->op(0)));
 
    if (is_exactly_a<su3d>(other->op(0))) {
 
        // Find the dummy indices of the contraction
        exvector self_indices = ex_to<indexed>(*self).get_indices();
        exvector other_indices = ex_to<indexed>(*other).get_indices();
        exvector all_indices = self_indices;
        all_indices.insert(all_indices.end(), other_indices.begin(), other_indices.end());
        exvector free_indices, dummy_indices;
        find_free_and_dummy(all_indices, free_indices, dummy_indices);
 
        // d.abc d.abc = 40/3
        if (dummy_indices.size() == 3) {
            *self = numeric(40, 3);
            *other = _ex1;
            return true;
 
        // d.akl d.bkl = 5/3 delta.ab
        } else if (dummy_indices.size() == 2) {
            exvector a;
            std::back_insert_iterator<exvector> ita(a);
            ita = set_difference(self_indices.begin(), self_indices.end(), dummy_indices.begin(), dummy_indices.end(), ita, ex_is_less());
            ita = set_difference(other_indices.begin(), other_indices.end(), dummy_indices.begin(), dummy_indices.end(), ita, ex_is_less());
            GINAC_ASSERT(a.size() == 2);
            *self = numeric(5, 3) * delta_tensor(a[0], a[1]);
            *other = _ex1;
            return true;
        }
 
    } else if (is_exactly_a<su3t>(other->op(0))) {
 
        // d.abc T.b T.c = 5/6 T.a
        if (other+1 != v.end()
         && is_exactly_a<su3t>(other[1].op(0))
         && ex_to<indexed>(*self).has_dummy_index_for(other[1].op(1))) {
 
            exvector self_indices = ex_to<indexed>(*self).get_indices();
            exvector dummy_indices = {other[0].op(1), other[1].op(1)};
            int sig;
            ex a = permute_free_index_to_front(self_indices, dummy_indices, sig);
            *self = numeric(5, 6);
            other[0] = color_T(a, ex_to<color>(other[0]).get_representation_label());
            other[1] = _ex1;
            return true;
        }
    }
 
    return false;
}
 
bool su3f::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
{
    GINAC_ASSERT(is_a<indexed>(*self));
    GINAC_ASSERT(is_a<indexed>(*other));
    GINAC_ASSERT(self->nops() == 4);
    GINAC_ASSERT(is_a<su3f>(self->op(0)));
 
    if (is_exactly_a<su3f>(other->op(0))) { // f*d is handled by su3d class
 
        // Find the dummy indices of the contraction
        exvector dummy_indices;
        dummy_indices = ex_to<indexed>(*self).get_dummy_indices(ex_to<indexed>(*other));
 
        // f.abc f.abc = 24
        if (dummy_indices.size() == 3) {
            *self = 24;
            *other = _ex1;
            return true;
 
        // f.akl f.bkl = 3 delta.ab
        } else if (dummy_indices.size() == 2) {
            int sign1, sign2;
            ex a = permute_free_index_to_front(ex_to<indexed>(*self).get_indices(), dummy_indices, sign1);
            ex b = permute_free_index_to_front(ex_to<indexed>(*other).get_indices(), dummy_indices, sign2);
            *self = sign1 * sign2 * 3 * delta_tensor(a, b);
            *other = _ex1;
            return true;
        }
 
    } else if (is_exactly_a<su3t>(other->op(0))) {
 
        // f.abc T.b T.c = 3/2 I T.a
        if (other+1 != v.end()
         && is_exactly_a<su3t>(other[1].op(0))
         && ex_to<indexed>(*self).has_dummy_index_for(other[1].op(1))) {
 
            exvector self_indices = ex_to<indexed>(*self).get_indices();
            exvector dummy_indices = {other[0].op(1), other[1].op(1)};
            int sig;
            ex a = permute_free_index_to_front(self_indices, dummy_indices, sig);
            *self = numeric(3, 2) * sig * I;
            other[0] = color_T(a, ex_to<color>(other[0]).get_representation_label());
            other[1] = _ex1;
            return true;
        }
    }
 
    return false;
}
 
// global functions
 
ex color_ONE(unsigned char rl)
{
    static ex ONE = dynallocate<su3one>();
    return color(ONE, rl);
}
 
ex color_T(const ex & a, unsigned char rl)
{
    static ex t = dynallocate<su3t>();
 
    if (!is_a<idx>(a))
        throw(std::invalid_argument("indices of color_T must be of type idx"));
    if (!ex_to<idx>(a).get_dim().is_equal(8))
        throw(std::invalid_argument("index dimension for color_T must be 8"));
 
    return color(t, a, rl);
}
 
ex color_f(const ex & a, const ex & b, const ex & c)
{
    static ex f = dynallocate<su3f>();
 
    if (!is_a<idx>(a) || !is_a<idx>(b) || !is_a<idx>(c))
        throw(std::invalid_argument("indices of color_f must be of type idx"));
    if (!ex_to<idx>(a).get_dim().is_equal(8) || !ex_to<idx>(b).get_dim().is_equal(8) || !ex_to<idx>(c).get_dim().is_equal(8))
        throw(std::invalid_argument("index dimension for color_f must be 8"));
 
    return indexed(f, antisymmetric3(), a, b, c);
}
 
ex color_d(const ex & a, const ex & b, const ex & c)
{
    static ex d = dynallocate<su3d>();
 
    if (!is_a<idx>(a) || !is_a<idx>(b) || !is_a<idx>(c))
        throw(std::invalid_argument("indices of color_d must be of type idx"));
    if (!ex_to<idx>(a).get_dim().is_equal(8) || !ex_to<idx>(b).get_dim().is_equal(8) || !ex_to<idx>(c).get_dim().is_equal(8))
        throw(std::invalid_argument("index dimension for color_d must be 8"));
 
    return indexed(d, symmetric3(), a, b, c);
}
 
ex color_h(const ex & a, const ex & b, const ex & c)
{
    return color_d(a, b, c) + I * color_f(a, b, c);
}
 
static bool is_color_tinfo(const return_type_t& ti)
{
    return *(ti.tinfo) == typeid(color);
}
 
static unsigned char get_representation_label(const return_type_t& ti)
{
    return (unsigned char)ti.rl;
}
 
ex color_trace(const ex & e, const std::set<unsigned char> & rls)
{
    if (is_a<color>(e)) {
 
        unsigned char rl = ex_to<color>(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 generators are traceless, except for color_ONE
        if (is_a<su3one>(e.op(0)))
            return _ex3;
        else
            return _ex0;
 
    } else if (is_exactly_a<mul>(e)) {
 
        // Trace of product: pull out non-color factors
        ex prod = _ex1;
        for (size_t i=0; i<e.nops(); i++) {
            const ex &o = e.op(i);
            if (is_color_tinfo(o.return_type_tinfo()))
                prod *= color_trace(o, rls);
            else
                prod *= o;
        }
        return prod;
 
    } else if (is_exactly_a<ncmul>(e)) {
 
        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;
 
        // Yes, expand product if necessary
        ex e_expanded = e.expand();
        if (!is_a<ncmul>(e_expanded))
            return color_trace(e_expanded, rls);
 
        size_t 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(dynallocate<symbol>(), 8);
 
            exvector v1;
            v1.reserve(num - 2);
            for (size_t 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;
        }
 
    } else if (e.nops() > 0) {
 
        // Trace maps to all other container classes (this includes sums)
        pointer_to_map_function_1arg<const std::set<unsigned char> &> fcn(color_trace, rls);
        return e.map(fcn);
 
    } else
        return _ex0;
}
 
ex color_trace(const ex & e, const lst & rll)
{
    // Convert list to set
    std::set<unsigned char> rls;
    for (auto & it : rll) {
        if (it.info(info_flags::nonnegint))
            rls.insert(ex_to<numeric>(it).to_int());
    }
 
    return color_trace(e, rls);
}
 
ex color_trace(const ex & e, unsigned char rl)
{
    // Convert label to set
    std::set<unsigned char> rls;
    rls.insert(rl);
 
    return color_trace(e, rls);
}
 
} // namespace GiNaC