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