ginac/color.cpp

   1 /** @file color.cpp
   2  *
   3  *  Implementation of GiNaC's color (SU(3) Lie algebra) objects. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
   7  *
   8  *  This program is free software; you can redistribute it and/or modify
   9  *  it under the terms of the GNU General Public License as published by
  10  *  the Free Software Foundation; either version 2 of the License, or
  11  *  (at your option) any later version.
  12  *
  13  *  This program is distributed in the hope that it will be useful,
  14  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
  15  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  16  *  GNU General Public License for more details.
  17  *
  18  *  You should have received a copy of the GNU General Public License
  19  *  along with this program; if not, write to the Free Software
  20  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
  21  */
  22
  23 #include <algorithm>
  24 #include <stdexcept>
  25
  26 #include "color.h"
  27 #include "ex.h"
  28 #include "idx.h"
  29 #include "ncmul.h"
  30 #include "numeric.h"
  31 #include "power.h" // for sqrt()
  32 #include "print.h"
  33 #include "archive.h"
  34 #include "debugmsg.h"
  35 #include "utils.h"
  36
  37 namespace GiNaC {
  38
  39 GINAC_IMPLEMENT_REGISTERED_CLASS(color, indexed)
  40 GINAC_IMPLEMENT_REGISTERED_CLASS(su3one, tensor)
  41 GINAC_IMPLEMENT_REGISTERED_CLASS(su3t, tensor)
  42 GINAC_IMPLEMENT_REGISTERED_CLASS(su3f, tensor)
  43 GINAC_IMPLEMENT_REGISTERED_CLASS(su3d, tensor)
  44
  45 //////////
  46 // default constructor, destructor, copy constructor assignment operator and helpers
  47 //////////
  48
  49 color::color() : representation_label(0)
  50 {
  51         debugmsg("color default constructor", LOGLEVEL_CONSTRUCT);
  52         tinfo_key = TINFO_color;
  53 }
  54
  55 void color::copy(const color & other)
  56 {
  57         inherited::copy(other);
  58         representation_label = other.representation_label;
  59 }
  60
  61 DEFAULT_DESTROY(color)
  62 DEFAULT_CTORS(su3one)
  63 DEFAULT_CTORS(su3t)
  64 DEFAULT_CTORS(su3f)
  65 DEFAULT_CTORS(su3d)
  66
  67 //////////
  68 // other constructors
  69 //////////
  70
  71 /** Construct object without any color index. This constructor is for
  72  *  internal use only. Use the color_ONE() function instead.
  73  *  @see color_ONE */
  74 color::color(const ex & b, unsigned rl = 0) : inherited(b), representation_label(rl)
  75 {
  76         debugmsg("color constructor from ex,unsigned", LOGLEVEL_CONSTRUCT);
  77         tinfo_key = TINFO_color;
  78 }
  79
  80 /** Construct object with one color index. This constructor is for internal
  81  *  use only. Use the color_T() function instead.
  82  *  @see color_T */
  83 color::color(const ex & b, const ex & i1, unsigned rl = 0) : inherited(b, i1), representation_label(rl)
  84 {
  85         debugmsg("color constructor from ex,ex,unsigned", LOGLEVEL_CONSTRUCT);
  86         tinfo_key = TINFO_color;
  87 }
  88
  89 color::color(unsigned rl, const exvector & v, bool discardable) : inherited(indexed::unknown, v, discardable), representation_label(rl)
  90 {
  91         debugmsg("color constructor from unsigned,exvector", LOGLEVEL_CONSTRUCT);
  92         tinfo_key = TINFO_color;
  93 }
  94
  95 color::color(unsigned rl, exvector * vp) : inherited(indexed::unknown, vp), representation_label(rl)
  96 {
  97         debugmsg("color constructor from unsigned,exvector *", LOGLEVEL_CONSTRUCT);
  98         tinfo_key = TINFO_color;
  99 }
 100
 101 //////////
 102 // archiving
 103 //////////
 104
 105 color::color(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 106 {
 107         debugmsg("color constructor from archive_node", LOGLEVEL_CONSTRUCT);
 108         n.find_unsigned("representation", representation_label);
 109 }
 110
 111 void color::archive(archive_node &n) const
 112 {
 113         inherited::archive(n);
 114         n.add_unsigned("representation", representation_label);
 115 }
 116
 117 DEFAULT_UNARCHIVE(color)
 118 DEFAULT_ARCHIVING(su3one)
 119 DEFAULT_ARCHIVING(su3t)
 120 DEFAULT_ARCHIVING(su3f)
 121 DEFAULT_ARCHIVING(su3d)
 122
 123 //////////
 124 // functions overriding virtual functions from bases classes
 125 //////////
 126
 127 int color::compare_same_type(const basic & other) const
 128 {
 129         GINAC_ASSERT(other.tinfo() == TINFO_color);
 130         const color &o = static_cast<const color &>(other);
 131
 132         if (representation_label != o.representation_label) {
 133                 // different representation label
 134                 return representation_label < o.representation_label ? -1 : 1;
 135         }
 136
 137         return inherited::compare_same_type(other);
 138 }
 139
 140 DEFAULT_COMPARE(su3one)
 141 DEFAULT_COMPARE(su3t)
 142 DEFAULT_COMPARE(su3f)
 143 DEFAULT_COMPARE(su3d)
 144
 145 DEFAULT_PRINT(su3one, "ONE")
 146 DEFAULT_PRINT(su3t, "T")
 147 DEFAULT_PRINT(su3f, "f")
 148 DEFAULT_PRINT(su3d, "d")
 149
 150 /** Perform automatic simplification on noncommutative product of color
 151  *  objects. This removes superfluous ONEs. */
 152 ex color::simplify_ncmul(const exvector & v) const
 153 {
 154         //!! TODO: sort by representation label
 155         exvector s;
 156         s.reserve(v.size());
 157
 158         exvector::const_iterator it = v.begin(), itend = v.end();
 159         while (it != itend) {
 160                 if (!is_ex_of_type(it->op(0), su3one))
 161                         s.push_back(*it);
 162                 it++;
 163         }
 164
 165         if (s.size() == 0)
 166                 return color(su3one());
 167         else if (s.size() == v.size())
 168                 return simplified_ncmul(v);
 169         else
 170                 return simplified_ncmul(s);
 171 }
 172
 173 ex color::thisexprseq(const exvector & v) const
 174 {
 175         return color(representation_label, v);
 176 }
 177
 178 ex color::thisexprseq(exvector * vp) const
 179 {
 180         return color(representation_label, vp);
 181 }
 182
 183 /** Given a vector iv3 of three indices and a vector iv2 of two indices that
 184  *  is a subset of iv3, return the (free) index that is in iv3 but not in
 185  *  iv2 and the sign introduced by permuting that index to the front.
 186  *
 187  *  @param iv3 Vector of 3 indices
 188  *  @param iv2 Vector of 2 indices, must be a subset of iv3
 189  *  @param sig Returs sign introduced by index permutation
 190  *  @return the free index (the one that is in iv3 but not in iv2) */
 191 static ex permute_free_index_to_front(const exvector & iv3, const exvector & iv2, int & sig)
 192 {
 193         GINAC_ASSERT(iv3.size() == 3);
 194         GINAC_ASSERT(iv2.size() == 2);
 195
 196         sig = 1;
 197
 198 #define TEST_PERMUTATION(A,B,C,P) \
 199         if (iv3[B].is_equal(iv2[0]) && iv3[C].is_equal(iv2[1])) { \
 200                 sig = P; \
 201                 return iv3[A]; \
 202         }
 203
 204         TEST_PERMUTATION(0,1,2,  1);
 205         TEST_PERMUTATION(0,2,1, -1);
 206         TEST_PERMUTATION(1,0,2, -1);
 207         TEST_PERMUTATION(1,2,0,  1);
 208         TEST_PERMUTATION(2,0,1,  1);
 209         TEST_PERMUTATION(2,1,0, -1);
 210
 211         throw(std::logic_error("permute_free_index_to_front(): no valid permutation found"));
 212 }
 213
 214 /** Automatic symbolic evaluation of indexed symmetric structure constant. */
 215 ex su3d::eval_indexed(const basic & i) const
 216 {
 217         GINAC_ASSERT(is_of_type(i, indexed));
 218         GINAC_ASSERT(i.nops() == 4);
 219         GINAC_ASSERT(is_ex_of_type(i.op(0), su3d));
 220
 221         // Convolutions are zero
 222         if (static_cast<const indexed &>(i).get_dummy_indices().size() != 0)
 223                 return _ex0();
 224
 225         // Numeric evaluation
 226         if (static_cast<const indexed &>(i).all_index_values_are(info_flags::nonnegint)) {
 227
 228                 // Sort indices
 229                 int v[3];
 230                 for (unsigned j=0; j<3; j++)
 231                         v[j] = ex_to_numeric(ex_to_idx(i.op(j + 1)).get_value()).to_int();
 232                 if (v[0] > v[1]) std::swap(v[0], v[1]);
 233                 if (v[0] > v[2]) std::swap(v[0], v[2]);
 234                 if (v[1] > v[2]) std::swap(v[1], v[2]);
 235
 236 #define CMPINDICES(A,B,C) ((v[0] == (A)) && (v[1] == (B)) && (v[2] == (C)))
 237
 238                 // Check for non-zero elements
 239                 if (CMPINDICES(1,4,6) || CMPINDICES(1,5,7) || CMPINDICES(2,5,6)
 240                  || CMPINDICES(3,4,4) || CMPINDICES(3,5,5))
 241                         return _ex1_2();
 242                 else if (CMPINDICES(2,4,7) || CMPINDICES(3,6,6) || CMPINDICES(3,7,7))
 243                         return _ex_1_2();
 244                 else if (CMPINDICES(1,1,8) || CMPINDICES(2,2,8) || CMPINDICES(3,3,8))
 245                         return sqrt(_ex3())/3;
 246                 else if (CMPINDICES(8,8,8))
 247                         return -sqrt(_ex3())/3;
 248                 else if (CMPINDICES(4,4,8) || CMPINDICES(5,5,8)
 249                       || CMPINDICES(6,6,8) || CMPINDICES(7,7,8))
 250                         return -sqrt(_ex3())/6;
 251                 else
 252                         return _ex0();
 253         }
 254
 255         // No further simplifications
 256         return i.hold();
 257 }
 258
 259 /** Automatic symbolic evaluation of indexed antisymmetric structure constant. */
 260 ex su3f::eval_indexed(const basic & i) const
 261 {
 262         GINAC_ASSERT(is_of_type(i, indexed));
 263         GINAC_ASSERT(i.nops() == 4);
 264         GINAC_ASSERT(is_ex_of_type(i.op(0), su3f));
 265
 266         // Numeric evaluation
 267         if (static_cast<const indexed &>(i).all_index_values_are(info_flags::nonnegint)) {
 268
 269                 // Sort indices, remember permutation sign
 270                 int v[3];
 271                 for (unsigned j=0; j<3; j++)
 272                         v[j] = ex_to_numeric(ex_to_idx(i.op(j + 1)).get_value()).to_int();
 273                 int sign = 1;
 274                 if (v[0] > v[1]) { std::swap(v[0], v[1]); sign = -sign; }
 275                 if (v[0] > v[2]) { std::swap(v[0], v[2]); sign = -sign; }
 276                 if (v[1] > v[2]) { std::swap(v[1], v[2]); sign = -sign; }
 277
 278                 // Check for non-zero elements
 279                 if (CMPINDICES(1,2,3))
 280                         return sign;
 281                 else if (CMPINDICES(1,4,7) || CMPINDICES(2,4,6)
 282                       || CMPINDICES(2,5,7) || CMPINDICES(3,4,5))
 283                         return _ex1_2() * sign;
 284                 else if (CMPINDICES(1,5,6) || CMPINDICES(3,6,7))
 285                         return _ex_1_2() * sign;
 286                 else if (CMPINDICES(4,5,8) || CMPINDICES(6,7,8))
 287                         return sqrt(_ex3())/2 * sign;
 288                 else
 289                         return _ex0();
 290         }
 291
 292         // No further simplifications
 293         return i.hold();
 294 }
 295
 296
 297 /** Contraction of an indexed symmetric structure constant with something else. */
 298 bool su3d::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
 299 {
 300         GINAC_ASSERT(is_ex_of_type(*self, indexed));
 301         GINAC_ASSERT(is_ex_of_type(*other, indexed));
 302         GINAC_ASSERT(self->nops() == 4);
 303         GINAC_ASSERT(is_ex_of_type(self->op(0), su3d));
 304
 305         if (is_ex_exactly_of_type(other->op(0), su3d)) {
 306
 307                 // Find the dummy indices of the contraction
 308                 exvector dummy_indices;
 309                 dummy_indices = ex_to_indexed(*self).get_dummy_indices(ex_to_indexed(*other));
 310
 311                 // d.abc*d.abc=40/3
 312                 if (dummy_indices.size() == 3) {
 313                         *self = numeric(40, 3);
 314                         *other = _ex1();
 315                         return true;
 316
 317                 // d.akl*d.bkl=5/3*delta.ab
 318                 } else if (dummy_indices.size() == 2) {
 319                         exvector a = index_set_difference(ex_to_indexed(*self).get_indices(), dummy_indices);
 320                         exvector b = index_set_difference(ex_to_indexed(*other).get_indices(), dummy_indices);
 321                         GINAC_ASSERT(a.size() > 0);
 322                         GINAC_ASSERT(b.size() > 0);
 323                         *self = numeric(5, 3) * delta_tensor(a[0], b[0]);
 324                         *other = _ex1();
 325                         return true;
 326                 }
 327         }
 328
 329         return false;
 330 }
 331
 332 /** Contraction of an indexed antisymmetric structure constant with something else. */
 333 bool su3f::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
 334 {
 335         GINAC_ASSERT(is_ex_of_type(*self, indexed));
 336         GINAC_ASSERT(is_ex_of_type(*other, indexed));
 337         GINAC_ASSERT(self->nops() == 4);
 338         GINAC_ASSERT(is_ex_of_type(self->op(0), su3f));
 339
 340         if (is_ex_exactly_of_type(other->op(0), su3f)) { // f*d is handled by su3d class
 341
 342                 // Find the dummy indices of the contraction
 343                 exvector dummy_indices;
 344                 dummy_indices = ex_to_indexed(*self).get_dummy_indices(ex_to_indexed(*other));
 345
 346                 // f.abc*f.abc=24
 347                 if (dummy_indices.size() == 3) {
 348                         *self = 24;
 349                         *other = _ex1();
 350                         return true;
 351
 352                 // f.akl*f.bkl=3*delta.ab
 353                 } else if (dummy_indices.size() == 2) {
 354                         int sign1, sign2;
 355                         ex a = permute_free_index_to_front(ex_to_indexed(*self).get_indices(), dummy_indices, sign1);
 356                         ex b = permute_free_index_to_front(ex_to_indexed(*other).get_indices(), dummy_indices, sign2);
 357                         *self = sign1 * sign2 * 3 * delta_tensor(a, b);
 358                         *other = _ex1();
 359                         return true;
 360                 }
 361         }
 362
 363         return false;
 364 }
 365
 366 //////////
 367 // global functions
 368 //////////
 369
 370 ex color_ONE(unsigned rl)
 371 {
 372         return color(su3one(), rl);
 373 }
 374
 375 ex color_T(const ex & a, unsigned rl)
 376 {
 377         if (!is_ex_of_type(a, idx))
 378                 throw(std::invalid_argument("indices of color_T must be of type idx"));
 379         if (!ex_to_idx(a).get_dim().is_equal(8))
 380                 throw(std::invalid_argument("index dimension for color_T must be 8"));
 381
 382         return color(su3t(), a, rl);
 383 }
 384
 385 ex color_f(const ex & a, const ex & b, const ex & c)
 386 {
 387         if (!is_ex_of_type(a, idx) || !is_ex_of_type(b, idx) || !is_ex_of_type(c, idx))
 388                 throw(std::invalid_argument("indices of color_f must be of type idx"));
 389         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))
 390                 throw(std::invalid_argument("index dimension for color_f must be 8"));
 391
 392         return indexed(su3f(), indexed::antisymmetric, a, b, c);
 393 }
 394
 395 ex color_d(const ex & a, const ex & b, const ex & c)
 396 {
 397         if (!is_ex_of_type(a, idx) || !is_ex_of_type(b, idx) || !is_ex_of_type(c, idx))
 398                 throw(std::invalid_argument("indices of color_d must be of type idx"));
 399         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))
 400                 throw(std::invalid_argument("index dimension for color_d must be 8"));
 401
 402         return indexed(su3d(), indexed::symmetric, a, b, c);
 403 }
 404
 405 ex color_h(const ex & a, const ex & b, const ex & c)
 406 {
 407         return color_d(a, b, c) + I * color_f(a, b, c);
 408 }
 409
 410 } // namespace GiNaC