X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fcolor.cpp;h=1d006e495dc3421df2913e39cfc9d705ec4ddfd1;hp=cd3179ae65cab408a506668859e5b25176bd0898;hb=2bf56ec52a7bed4ac3d02be8887b0287b5acd189;hpb=f79efd6115f09fd1d4fbb42d25b506f6553b1a36 diff --git a/ginac/color.cpp b/ginac/color.cpp index cd3179ae..1d006e49 100644 --- a/ginac/color.cpp +++ b/ginac/color.cpp @@ -3,7 +3,7 @@ * Implementation of GiNaC's color (SU(3) Lie algebra) objects. */ /* - * GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2015 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 @@ -17,46 +17,56 @@ * * 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., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA + * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA */ #include "color.h" -#include "ex.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 "debugmsg.h" #include "utils.h" +#include +#include + namespace GiNaC { GINAC_IMPLEMENT_REGISTERED_CLASS(color, indexed) -GINAC_IMPLEMENT_REGISTERED_CLASS(su3one, tensor) -GINAC_IMPLEMENT_REGISTERED_CLASS(su3t, tensor) -GINAC_IMPLEMENT_REGISTERED_CLASS(su3f, tensor) -GINAC_IMPLEMENT_REGISTERED_CLASS(su3d, tensor) + +GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(su3one, tensor, + print_func(&su3one::do_print). + print_func(&su3one::do_print_latex)) + +GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(su3t, tensor, + print_func(&su3t::do_print). + print_func(&su3t::do_print)) + +GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(su3f, tensor, + print_func(&su3f::do_print). + print_func(&su3f::do_print)) + +GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(su3d, tensor, + print_func(&su3d::do_print). + print_func(&su3d::do_print)) ////////// -// default constructor, destructor, copy constructor assignment operator and helpers +// default constructors ////////// color::color() : representation_label(0) { - debugmsg("color default constructor", LOGLEVEL_CONSTRUCT); - tinfo_key = TINFO_color; } -void color::copy(const color & other) -{ - inherited::copy(other); - representation_label = other.representation_label; -} - -DEFAULT_DESTROY(color) -DEFAULT_CTORS(su3one) -DEFAULT_CTORS(su3t) -DEFAULT_CTORS(su3f) -DEFAULT_CTORS(su3d) +DEFAULT_CTOR(su3one) +DEFAULT_CTOR(su3t) +DEFAULT_CTOR(su3f) +DEFAULT_CTOR(su3d) ////////// // other constructors @@ -65,62 +75,61 @@ DEFAULT_CTORS(su3d) /** 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 = 0) : 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); - 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 = 0) : inherited(b, i1), 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, bool discardable) : inherited(not_symmetric(), v, discardable), representation_label(rl) { - debugmsg("color constructor from ex,ex,unsigned", 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, exvector && v) : inherited(not_symmetric(), std::move(v)), representation_label(rl) { - debugmsg("color constructor from unsigned,exvector", LOGLEVEL_CONSTRUCT); - tinfo_key = TINFO_color; } -color::color(unsigned rl, exvector * vp) : inherited(indexed::unknown, vp), representation_label(rl) +return_type_t color::return_type_tinfo() const { - debugmsg("color constructor from unsigned,exvector *", LOGLEVEL_CONSTRUCT); - tinfo_key = TINFO_color; + return make_return_type_t(representation_label); } ////////// // archiving ////////// -color::color(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst) +void color::read_archive(const archive_node& n, lst& sym_lst) { - debugmsg("color constructor from archive_node", LOGLEVEL_CONSTRUCT); - n.find_unsigned("representation", representation_label); + 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("representation", representation_label); + n.add_unsigned("label", representation_label); } -DEFAULT_UNARCHIVE(color) -DEFAULT_ARCHIVING(su3one) -DEFAULT_ARCHIVING(su3t) -DEFAULT_ARCHIVING(su3f) -DEFAULT_ARCHIVING(su3d) +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 bases classes +// functions overriding virtual functions from base classes ////////// int color::compare_same_type(const basic & other) const { - GINAC_ASSERT(other.tinfo() == TINFO_color); + GINAC_ASSERT(is_a(other)); const color &o = static_cast(other); if (representation_label != o.representation_label) { @@ -131,56 +140,378 @@ int color::compare_same_type(const basic & other) const return inherited::compare_same_type(other); } +bool color::match_same_type(const basic & other) const +{ + GINAC_ASSERT(is_a(other)); + const color &o = static_cast(other); + + return representation_label == o.representation_label; +} + DEFAULT_COMPARE(su3one) DEFAULT_COMPARE(su3t) DEFAULT_COMPARE(su3f) DEFAULT_COMPARE(su3d) -DEFAULT_PRINT(su3one, "ONE") +DEFAULT_PRINT_LATEX(su3one, "ONE", "\\mathbb{1}") DEFAULT_PRINT(su3t, "T") DEFAULT_PRINT(su3f, "f") DEFAULT_PRINT(su3d, "d") /** Perform automatic simplification on noncommutative product of color * objects. This removes superfluous ONEs. */ -ex color::simplify_ncmul(const exvector & v) const +ex color::eval_ncmul(const exvector & v) const { - //!! to be implemented - return nonsimplified_ncmul(v); + exvector s; + s.reserve(v.size()); + + // Remove superfluous ONEs + for (auto & it : v) { + if (!is_a(it.op(0))) + s.push_back(it); + } + + if (s.empty()) + return color(su3one(), representation_label); + else + return hold_ncmul(s); } -ex color::thisexprseq(const exvector & v) const +ex color::thiscontainer(const exvector & v) const { return color(representation_label, v); } -ex color::thisexprseq(exvector * vp) const +ex color::thiscontainer(exvector && v) const +{ + return color(representation_label, std::move(v)); +} + +/** Given a vector iv3 of three indices and a vector iv2 of two indices that + * is a subset of iv3, return the (free) index that is in iv3 but not in + * iv2 and the sign introduced by permuting that index to the front. + * + * @param iv3 Vector of 3 indices + * @param iv2 Vector of 2 indices, must be a subset of iv3 + * @param sig Returns sign introduced by index permutation + * @return the free index (the one that is in iv3 but not in iv2) */ +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")); +} + +/** Automatic symbolic evaluation of indexed symmetric structure constant. */ +ex su3d::eval_indexed(const basic & i) const +{ + GINAC_ASSERT(is_a(i)); + GINAC_ASSERT(i.nops() == 4); + GINAC_ASSERT(is_a(i.op(0))); + + // Convolutions are zero + if (!(static_cast(i).get_dummy_indices().empty())) + return _ex0; + + // Numeric evaluation + if (static_cast(i).all_index_values_are(info_flags::nonnegint)) { + + // Sort indices + int v[3]; + for (unsigned j=0; j<3; j++) + v[j] = ex_to(ex_to(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(); +} + +/** Automatic symbolic evaluation of indexed antisymmetric structure constant. */ +ex su3f::eval_indexed(const basic & i) const +{ + GINAC_ASSERT(is_a(i)); + GINAC_ASSERT(i.nops() == 4); + GINAC_ASSERT(is_a(i.op(0))); + + // Numeric evaluation + if (static_cast(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(ex_to(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(); +} + + +/** Contraction of generator with something else. */ +bool su3t::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const +{ + GINAC_ASSERT(is_a(*self)); + GINAC_ASSERT(is_a(*other)); + GINAC_ASSERT(self->nops() == 2); + GINAC_ASSERT(is_a(self->op(0))); + unsigned char rl = ex_to(*self).get_representation_label(); + + if (is_exactly_a(other->op(0))) { + + // Contraction only makes sense if the representation labels are equal + GINAC_ASSERT(is_a(*other)); + if (ex_to(*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(self[1])) { + *self = numeric(-1, 6); + *other = _ex1; + return true; + + // T.a S T.a = 1/2 Tr(S) - 1/6 S + } else { + exvector::iterator it = self + 1; + while (it != other) { + if (!is_a(*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; +} + +/** Contraction of an indexed symmetric structure constant with something else. */ +bool su3d::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const +{ + GINAC_ASSERT(is_a(*self)); + GINAC_ASSERT(is_a(*other)); + GINAC_ASSERT(self->nops() == 4); + GINAC_ASSERT(is_a(self->op(0))); + + if (is_exactly_a(other->op(0))) { + + // Find the dummy indices of the contraction + exvector self_indices = ex_to(*self).get_indices(); + exvector other_indices = ex_to(*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 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(other->op(0))) { + + // d.abc T.b T.c = 5/6 T.a + if (other+1 != v.end() + && is_exactly_a(other[1].op(0)) + && ex_to(*self).has_dummy_index_for(other[1].op(1))) { + + exvector self_indices = ex_to(*self).get_indices(); + exvector dummy_indices; + dummy_indices.push_back(other[0].op(1)); + dummy_indices.push_back(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(other[0]).get_representation_label()); + other[1] = _ex1; + return true; + } + } + + return false; +} + +/** Contraction of an indexed antisymmetric structure constant with something else. */ +bool su3f::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const { - return color(representation_label, vp); + GINAC_ASSERT(is_a(*self)); + GINAC_ASSERT(is_a(*other)); + GINAC_ASSERT(self->nops() == 4); + GINAC_ASSERT(is_a(self->op(0))); + + if (is_exactly_a(other->op(0))) { // f*d is handled by su3d class + + // Find the dummy indices of the contraction + exvector dummy_indices; + dummy_indices = ex_to(*self).get_dummy_indices(ex_to(*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(*self).get_indices(), dummy_indices, sign1); + ex b = permute_free_index_to_front(ex_to(*other).get_indices(), dummy_indices, sign2); + *self = sign1 * sign2 * 3 * delta_tensor(a, b); + *other = _ex1; + return true; + } + + } else if (is_exactly_a(other->op(0))) { + + // f.abc T.b T.c = 3/2 I T.a + if (other+1 != v.end() + && is_exactly_a(other[1].op(0)) + && ex_to(*self).has_dummy_index_for(other[1].op(1))) { + + exvector self_indices = ex_to(*self).get_indices(); + exvector dummy_indices; + dummy_indices.push_back(other[0].op(1)); + dummy_indices.push_back(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(other[0]).get_representation_label()); + other[1] = _ex1; + return true; + } + } + + return false; } ////////// // global functions ////////// -ex color_ONE(unsigned rl) +ex color_ONE(unsigned char rl) { - return color(su3one(), rl); + static ex ONE = (new su3one)->setflag(status_flags::dynallocated); + return color(ONE, rl); } -ex color_T(const ex & a, unsigned rl) +ex color_T(const ex & a, unsigned char rl) { - return color(su3t(), a, rl); + static ex t = (new su3t)->setflag(status_flags::dynallocated); + + if (!is_a(a)) + throw(std::invalid_argument("indices of color_T must be of type idx")); + if (!ex_to(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) { - return indexed(su3f(), indexed::antisymmetric, a, b, c); + static ex f = (new su3f)->setflag(status_flags::dynallocated); + + if (!is_a(a) || !is_a(b) || !is_a(c)) + throw(std::invalid_argument("indices of color_f must be of type idx")); + if (!ex_to(a).get_dim().is_equal(8) || !ex_to(b).get_dim().is_equal(8) || !ex_to(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) { - return indexed(su3d(), indexed::symmetric, a, b, c); + static ex d = (new su3d)->setflag(status_flags::dynallocated); + + if (!is_a(a) || !is_a(b) || !is_a(c)) + throw(std::invalid_argument("indices of color_d must be of type idx")); + if (!ex_to(a).get_dim().is_equal(8) || !ex_to(b).get_dim().is_equal(8) || !ex_to(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) @@ -188,4 +519,125 @@ ex color_h(const ex & a, const ex & b, const ex & c) 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 an arbitrary representation label). */ +static bool is_color_tinfo(const return_type_t& ti) +{ + return *(ti.tinfo) == typeid(color); +} + +/** Extract representation label from tinfo key (as returned by + * return_type_tinfo()). */ +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 & rls) +{ + if (is_a(e)) { + + unsigned char rl = ex_to(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(e.op(0))) + return _ex3; + else + return _ex0; + + } else if (is_exactly_a(e)) { + + // Trace of product: pull out non-color factors + ex prod = _ex1; + for (size_t i=0; i(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(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((new symbol)->setflag(status_flags::dynallocated), 8); + + exvector v1; + v1.reserve(num - 2); + for (size_t i=0; i 0) { + + // Trace maps to all other container classes (this includes sums) + pointer_to_map_function_1arg &> 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 rls; + for (auto & it : rll) { + if (it.info(info_flags::nonnegint)) + rls.insert(ex_to(it).to_int()); + } + + return color_trace(e, rls); +} + +ex color_trace(const ex & e, unsigned char rl) +{ + // Convert label to set + std::set rls; + rls.insert(rl); + + return color_trace(e, rls); +} + } // namespace GiNaC