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 "archive.h"
  33 #include "debugmsg.h"
  34 #include "utils.h"
  35
  36 namespace GiNaC {
  37
  38 GINAC_IMPLEMENT_REGISTERED_CLASS(color, indexed)
  39 GINAC_IMPLEMENT_REGISTERED_CLASS(su3one, tensor)
  40 GINAC_IMPLEMENT_REGISTERED_CLASS(su3t, tensor)
  41 GINAC_IMPLEMENT_REGISTERED_CLASS(su3f, tensor)
  42 GINAC_IMPLEMENT_REGISTERED_CLASS(su3d, tensor)
  43
  44 //////////
  45 // default constructor, destructor, copy constructor assignment operator and helpers
  46 //////////
  47
  48 color::color() : representation_label(0)
  49 {
  50         debugmsg("color default constructor", LOGLEVEL_CONSTRUCT);
  51         tinfo_key = TINFO_color;
  52 }
  53
  54 void color::copy(const color & other)
  55 {
  56         inherited::copy(other);
  57         representation_label = other.representation_label;
  58 }
  59
  60 DEFAULT_DESTROY(color)
  61 DEFAULT_CTORS(su3one)
  62 DEFAULT_CTORS(su3t)
  63 DEFAULT_CTORS(su3f)
  64 DEFAULT_CTORS(su3d)
  65
  66 //////////
  67 // other constructors
  68 //////////
  69
  70 /** Construct object without any color index. This constructor is for
  71  *  internal use only. Use the color_ONE() function instead.
  72  *  @see color_ONE */
  73 color::color(const ex & b, unsigned rl = 0) : inherited(b), representation_label(rl)
  74 {
  75         debugmsg("color constructor from ex,unsigned", LOGLEVEL_CONSTRUCT);
  76         tinfo_key = TINFO_color;
  77 }
  78
  79 /** Construct object with one color index. This constructor is for internal
  80  *  use only. Use the color_T() function instead.
  81  *  @see color_T */
  82 color::color(const ex & b, const ex & i1, unsigned rl = 0) : inherited(b, i1), representation_label(rl)
  83 {
  84         debugmsg("color constructor from ex,ex,unsigned", LOGLEVEL_CONSTRUCT);
  85         tinfo_key = TINFO_color;
  86 }
  87
  88 color::color(unsigned rl, const exvector & v, bool discardable) : inherited(indexed::unknown, v, discardable), representation_label(rl)
  89 {
  90         debugmsg("color constructor from unsigned,exvector", LOGLEVEL_CONSTRUCT);
  91         tinfo_key = TINFO_color;
  92 }
  93
  94 color::color(unsigned rl, exvector * vp) : inherited(indexed::unknown, vp), representation_label(rl)
  95 {
  96         debugmsg("color constructor from unsigned,exvector *", LOGLEVEL_CONSTRUCT);
  97         tinfo_key = TINFO_color;
  98 }
  99
 100 //////////
 101 // archiving
 102 //////////
 103
 104 color::color(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 105 {
 106         debugmsg("color constructor from archive_node", LOGLEVEL_CONSTRUCT);
 107         n.find_unsigned("representation", representation_label);
 108 }
 109
 110 void color::archive(archive_node &n) const
 111 {
 112         inherited::archive(n);
 113         n.add_unsigned("representation", representation_label);
 114 }
 115
 116 DEFAULT_UNARCHIVE(color)
 117 DEFAULT_ARCHIVING(su3one)
 118 DEFAULT_ARCHIVING(su3t)
 119 DEFAULT_ARCHIVING(su3f)
 120 DEFAULT_ARCHIVING(su3d)
 121
 122 //////////
 123 // functions overriding virtual functions from bases classes
 124 //////////
 125
 126 int color::compare_same_type(const basic & other) const
 127 {
 128         GINAC_ASSERT(other.tinfo() == TINFO_color);
 129         const color &o = static_cast<const color &>(other);
 130
 131         if (representation_label != o.representation_label) {
 132                 // different representation label
 133                 return representation_label < o.representation_label ? -1 : 1;
 134         }
 135
 136         return inherited::compare_same_type(other);
 137 }
 138
 139 DEFAULT_COMPARE(su3one)
 140 DEFAULT_COMPARE(su3t)
 141 DEFAULT_COMPARE(su3f)
 142 DEFAULT_COMPARE(su3d)
 143
 144 DEFAULT_PRINT(su3one, "ONE")
 145 DEFAULT_PRINT(su3t, "T")
 146 DEFAULT_PRINT(su3f, "f")
 147 DEFAULT_PRINT(su3d, "d")
 148
 149 /** Perform automatic simplification on noncommutative product of color
 150  *  objects. This removes superfluous ONEs. */
 151 ex color::simplify_ncmul(const exvector & v) const
 152 {
 153         //!! TODO: sort by representation label
 154         exvector s;
 155         s.reserve(v.size());
 156
 157         exvector::const_iterator it = v.begin(), itend = v.end();
 158         while (it != itend) {
 159                 if (!is_ex_of_type(it->op(0), su3one))
 160                         s.push_back(*it);
 161                 it++;
 162         }
 163
 164         if (s.size() == 0)
 165                 return color(su3one());
 166         else if (s.size() == v.size())
 167                 return simplified_ncmul(v);
 168         else
 169                 return simplified_ncmul(s);
 170 }
 171
 172 ex color::thisexprseq(const exvector & v) const
 173 {
 174         return color(representation_label, v);
 175 }
 176
 177 ex color::thisexprseq(exvector * vp) const
 178 {
 179         return color(representation_label, vp);
 180 }
 181
 182 /** Given a vector iv3 of three indices and a vector iv2 of two indices that
 183  *  is a subset of iv3, return the (free) index that is in iv3 but not in
 184  *  iv2 and the sign introduced by permuting that index to the front.
 185  *
 186  *  @param iv3 Vector of 3 indices
 187  *  @param iv2 Vector of 2 indices, must be a subset of iv3
 188  *  @param sig Returs sign introduced by index permutation
 189  *  @return the free index (the one that is in iv3 but not in iv2) */
 190 static ex permute_free_index_to_front(const exvector & iv3, const exvector & iv2, int & sig)
 191 {
 192         GINAC_ASSERT(iv3.size() == 3);
 193         GINAC_ASSERT(iv2.size() == 2);
 194
 195         sig = 1;
 196
 197 #define TEST_PERMUTATION(A,B,C,P) \
 198         if (iv3[B].is_equal(iv2[0]) && iv3[C].is_equal(iv2[1])) { \
 199                 sig = P; \
 200                 return iv3[A]; \
 201         }
 202
 203         TEST_PERMUTATION(0,1,2,  1);
 204         TEST_PERMUTATION(0,2,1, -1);
 205         TEST_PERMUTATION(1,0,2, -1);
 206         TEST_PERMUTATION(1,2,0,  1);
 207         TEST_PERMUTATION(2,0,1,  1);
 208         TEST_PERMUTATION(2,1,0, -1);
 209
 210         throw(std::logic_error("permute_free_index_to_front(): no valid permutation found"));
 211 }
 212
 213 /** Automatic symbolic evaluation of indexed symmetric structure constant. */
 214 ex su3d::eval_indexed(const basic & i) const
 215 {
 216         GINAC_ASSERT(is_of_type(i, indexed));
 217         GINAC_ASSERT(i.nops() == 4);
 218         GINAC_ASSERT(is_ex_of_type(i.op(0), su3d));
 219
 220         // Convolutions are zero
 221         if (static_cast<const indexed &>(i).get_dummy_indices().size() != 0)
 222                 return _ex0();
 223
 224         // Numeric evaluation
 225         if (static_cast<const indexed &>(i).all_index_values_are(info_flags::nonnegint)) {
 226
 227                 // Sort indices
 228                 int v[3];
 229                 for (unsigned j=0; j<3; j++)
 230                         v[j] = ex_to_numeric(ex_to_idx(i.op(j + 1)).get_value()).to_int();
 231                 if (v[0] > v[1]) std::swap(v[0], v[1]);
 232                 if (v[0] > v[2]) std::swap(v[0], v[2]);
 233                 if (v[1] > v[2]) std::swap(v[1], v[2]);
 234
 235 #define CMPINDICES(A,B,C) ((v[0] == (A)) && (v[1] == (B)) && (v[2] == (C)))
 236
 237                 // Check for non-zero elements
 238                 if (CMPINDICES(1,4,6) || CMPINDICES(1,5,7) || CMPINDICES(2,5,6)
 239                  || CMPINDICES(3,4,4) || CMPINDICES(3,5,5))
 240                         return _ex1_2();
 241                 else if (CMPINDICES(2,4,7) || CMPINDICES(3,6,6) || CMPINDICES(3,7,7))
 242                         return _ex_1_2();
 243                 else if (CMPINDICES(1,1,8) || CMPINDICES(2,2,8) || CMPINDICES(3,3,8))
 244                         return sqrt(_ex3())/3;
 245                 else if (CMPINDICES(8,8,8))
 246                         return -sqrt(_ex3())/3;
 247                 else if (CMPINDICES(4,4,8) || CMPINDICES(5,5,8)
 248                       || CMPINDICES(6,6,8) || CMPINDICES(7,7,8))
 249                         return -sqrt(_ex3())/6;
 250                 else
 251                         return _ex0();
 252         }
 253
 254         // No further simplifications
 255         return i.hold();
 256 }
 257
 258 /** Automatic symbolic evaluation of indexed antisymmetric structure constant. */
 259 ex su3f::eval_indexed(const basic & i) const
 260 {
 261         GINAC_ASSERT(is_of_type(i, indexed));
 262         GINAC_ASSERT(i.nops() == 4);
 263         GINAC_ASSERT(is_ex_of_type(i.op(0), su3f));
 264
 265         // Numeric evaluation
 266         if (static_cast<const indexed &>(i).all_index_values_are(info_flags::nonnegint)) {
 267
 268                 // Sort indices, remember permutation sign
 269                 int v[3];
 270                 for (unsigned j=0; j<3; j++)
 271                         v[j] = ex_to_numeric(ex_to_idx(i.op(j + 1)).get_value()).to_int();
 272                 int sign = 1;
 273                 if (v[0] > v[1]) { std::swap(v[0], v[1]); sign = -sign; }
 274                 if (v[0] > v[2]) { std::swap(v[0], v[2]); sign = -sign; }
 275                 if (v[1] > v[2]) { std::swap(v[1], v[2]); sign = -sign; }
 276
 277                 // Check for non-zero elements
 278                 if (CMPINDICES(1,2,3))
 279                         return sign;
 280                 else if (CMPINDICES(1,4,7) || CMPINDICES(2,4,6)
 281                       || CMPINDICES(2,5,7) || CMPINDICES(3,4,5))
 282                         return _ex1_2() * sign;
 283                 else if (CMPINDICES(1,5,6) || CMPINDICES(3,6,7))
 284                         return _ex_1_2() * sign;
 285                 else if (CMPINDICES(4,5,8) || CMPINDICES(6,7,8))
 286                         return sqrt(_ex3())/2 * sign;
 287                 else
 288                         return _ex0();
 289         }
 290
 291         // No further simplifications
 292         return i.hold();
 293 }
 294
 295
 296 /** Contraction of an indexed symmetric structure constant with something else. */
 297 bool su3d::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
 298 {
 299         GINAC_ASSERT(is_ex_of_type(*self, indexed));
 300         GINAC_ASSERT(is_ex_of_type(*other, indexed));
 301         GINAC_ASSERT(self->nops() == 4);
 302         GINAC_ASSERT(is_ex_of_type(self->op(0), su3d));
 303
 304         if (is_ex_exactly_of_type(other->op(0), su3d) || is_ex_exactly_of_type(other->op(0), su3f)) {
 305
 306                 // Find the dummy indices of the contraction
 307                 exvector dummy_indices;
 308                 dummy_indices = ex_to_indexed(*self).get_dummy_indices(ex_to_indexed(*other));
 309
 310                 if (is_ex_exactly_of_type(other->op(0), su3d)) {
 311
 312                         // d.abc*d.abc=40/3
 313                         if (dummy_indices.size() == 3) {
 314                                 *self = numeric(40, 3);
 315                                 *other = _ex1();
 316                                 return true;
 317
 318                         // d.akl*d.bkl=5/3*delta.ab
 319                         } else if (dummy_indices.size() == 2) {
 320                                 exvector a = index_set_difference(ex_to_indexed(*self).get_indices(), dummy_indices);
 321                                 exvector b = index_set_difference(ex_to_indexed(*other).get_indices(), dummy_indices);
 322                                 GINAC_ASSERT(a.size() > 0);
 323                                 GINAC_ASSERT(b.size() > 0);
 324                                 *self = numeric(5, 3) * delta_tensor(a[0], b[0]);
 325                                 *other = _ex1();
 326                                 return true;
 327                         }
 328
 329                 } else {
 330
 331                         // d.akl*f.bkl=0 (includes the case a=b)
 332                         if (dummy_indices.size() >= 2) {
 333                                 *self = _ex0();
 334                                 *other = _ex0();
 335                                 return true;
 336                         }
 337                 }
 338         }
 339
 340         return false;
 341 }
 342
 343 /** Contraction of an indexed antisymmetric structure constant with something else. */
 344 bool su3f::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
 345 {
 346         GINAC_ASSERT(is_ex_of_type(*self, indexed));
 347         GINAC_ASSERT(is_ex_of_type(*other, indexed));
 348         GINAC_ASSERT(self->nops() == 4);
 349         GINAC_ASSERT(is_ex_of_type(self->op(0), su3f));
 350
 351         if (is_ex_exactly_of_type(other->op(0), su3f)) { // f*d is handled by su3d class
 352
 353                 // Find the dummy indices of the contraction
 354                 exvector dummy_indices;
 355                 dummy_indices = ex_to_indexed(*self).get_dummy_indices(ex_to_indexed(*other));
 356
 357                 // f.abc*f.abc=24
 358                 if (dummy_indices.size() == 3) {
 359                         *self = 24;
 360                         *other = _ex1();
 361                         return true;
 362
 363                 // f.akl*f.bkl=3*delta.ab
 364                 } else if (dummy_indices.size() == 2) {
 365                         int sign1, sign2;
 366                         ex a = permute_free_index_to_front(ex_to_indexed(*self).get_indices(), dummy_indices, sign1);
 367                         ex b = permute_free_index_to_front(ex_to_indexed(*other).get_indices(), dummy_indices, sign2);
 368                         *self = sign1 * sign2 * 3 * delta_tensor(a, b);
 369                         *other = _ex1();
 370                         return true;
 371                 }
 372         }
 373
 374         return false;
 375 }
 376
 377 //////////
 378 // global functions
 379 //////////
 380
 381 ex color_ONE(unsigned rl)
 382 {
 383         return color(su3one(), rl);
 384 }
 385
 386 ex color_T(const ex & a, unsigned rl)
 387 {
 388         if (!is_ex_of_type(a, idx))
 389                 throw(std::invalid_argument("indices of color_T must be of type idx"));
 390         if (!ex_to_idx(a).get_dim().is_equal(8))
 391                 throw(std::invalid_argument("index dimension for color_T must be 8"));
 392
 393         return color(su3t(), a, rl);
 394 }
 395
 396 ex color_f(const ex & a, const ex & b, const ex & c)
 397 {
 398         if (!is_ex_of_type(a, idx) || !is_ex_of_type(b, idx) || !is_ex_of_type(c, idx))
 399                 throw(std::invalid_argument("indices of color_f must be of type idx"));
 400         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))
 401                 throw(std::invalid_argument("index dimension for color_f must be 8"));
 402
 403         return indexed(su3f(), indexed::antisymmetric, a, b, c);
 404 }
 405
 406 ex color_d(const ex & a, const ex & b, const ex & c)
 407 {
 408         if (!is_ex_of_type(a, idx) || !is_ex_of_type(b, idx) || !is_ex_of_type(c, idx))
 409                 throw(std::invalid_argument("indices of color_d must be of type idx"));
 410         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))
 411                 throw(std::invalid_argument("index dimension for color_d must be 8"));
 412
 413         return indexed(su3d(), indexed::symmetric, a, b, c);
 414 }
 415
 416 ex color_h(const ex & a, const ex & b, const ex & c)
 417 {
 418         return color_d(a, b, c) + I * color_f(a, b, c);
 419 }
 420
 421 } // namespace GiNaC