ginac/clifford.cpp

   1 /** @file clifford.cpp
   2  *
   3  *  Implementation of GiNaC's clifford algebra (Dirac gamma) 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 "clifford.h"
  24 #include "ex.h"
  25 #include "idx.h"
  26 #include "ncmul.h"
  27 #include "print.h"
  28 #include "archive.h"
  29 #include "debugmsg.h"
  30 #include "utils.h"
  31
  32 #include <stdexcept>
  33
  34 namespace GiNaC {
  35
  36 GINAC_IMPLEMENT_REGISTERED_CLASS(clifford, indexed)
  37 GINAC_IMPLEMENT_REGISTERED_CLASS(diracone, tensor)
  38 GINAC_IMPLEMENT_REGISTERED_CLASS(diracgamma, tensor)
  39 GINAC_IMPLEMENT_REGISTERED_CLASS(diracgamma5, tensor)
  40
  41 //////////
  42 // default constructor, destructor, copy constructor assignment operator and helpers
  43 //////////
  44
  45 clifford::clifford() : representation_label(0)
  46 {
  47         debugmsg("clifford default constructor", LOGLEVEL_CONSTRUCT);
  48         tinfo_key = TINFO_clifford;
  49 }
  50
  51 void clifford::copy(const clifford & other)
  52 {
  53         inherited::copy(other);
  54         representation_label = other.representation_label;
  55 }
  56
  57 DEFAULT_DESTROY(clifford)
  58 DEFAULT_CTORS(diracone)
  59 DEFAULT_CTORS(diracgamma)
  60 DEFAULT_CTORS(diracgamma5)
  61
  62 //////////
  63 // other constructors
  64 //////////
  65
  66 /** Construct object without any indices. This constructor is for internal
  67  *  use only. Use the dirac_ONE() function instead.
  68  *  @see dirac_ONE */
  69 clifford::clifford(const ex & b, unsigned char rl) : inherited(b), representation_label(rl)
  70 {
  71         debugmsg("clifford constructor from ex", LOGLEVEL_CONSTRUCT);
  72         tinfo_key = TINFO_clifford;
  73 }
  74
  75 /** Construct object with one Lorentz index. This constructor is for internal
  76  *  use only. Use the dirac_gamma() function instead.
  77  *  @see dirac_gamma */
  78 clifford::clifford(const ex & b, const ex & mu, unsigned char rl) : inherited(b, mu), representation_label(rl)
  79 {
  80         debugmsg("clifford constructor from ex,ex", LOGLEVEL_CONSTRUCT);
  81         GINAC_ASSERT(is_ex_of_type(mu, varidx));
  82         tinfo_key = TINFO_clifford;
  83 }
  84
  85 clifford::clifford(unsigned char rl, const exvector & v, bool discardable) : inherited(indexed::unknown, v, discardable), representation_label(rl)
  86 {
  87         debugmsg("clifford constructor from unsigned char,exvector", LOGLEVEL_CONSTRUCT);
  88         tinfo_key = TINFO_clifford;
  89 }
  90
  91 clifford::clifford(unsigned char rl, exvector * vp) : inherited(indexed::unknown, vp), representation_label(rl)
  92 {
  93         debugmsg("clifford constructor from unsigned char,exvector *", LOGLEVEL_CONSTRUCT);
  94         tinfo_key = TINFO_clifford;
  95 }
  96
  97 //////////
  98 // archiving
  99 //////////
 100
 101 clifford::clifford(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 102 {
 103         debugmsg("clifford constructor from archive_node", LOGLEVEL_CONSTRUCT);
 104         unsigned rl;
 105         n.find_unsigned("label", rl);
 106         representation_label = rl;
 107 }
 108
 109 void clifford::archive(archive_node &n) const
 110 {
 111         inherited::archive(n);
 112         n.add_unsigned("label", representation_label);
 113 }
 114
 115 DEFAULT_UNARCHIVE(clifford)
 116 DEFAULT_ARCHIVING(diracone)
 117 DEFAULT_ARCHIVING(diracgamma)
 118 DEFAULT_ARCHIVING(diracgamma5)
 119
 120 //////////
 121 // functions overriding virtual functions from bases classes
 122 //////////
 123
 124 int clifford::compare_same_type(const basic & other) const
 125 {
 126         GINAC_ASSERT(other.tinfo() == TINFO_clifford);
 127         const clifford &o = static_cast<const clifford &>(other);
 128
 129         if (representation_label != o.representation_label) {
 130                 // different representation label
 131                 return representation_label < o.representation_label ? -1 : 1;
 132         }
 133
 134         return inherited::compare_same_type(other);
 135 }
 136
 137 DEFAULT_COMPARE(diracone)
 138 DEFAULT_COMPARE(diracgamma)
 139 DEFAULT_COMPARE(diracgamma5)
 140
 141 DEFAULT_PRINT(diracone, "ONE")
 142 DEFAULT_PRINT(diracgamma, "gamma")
 143 DEFAULT_PRINT(diracgamma5, "gamma5")
 144
 145 /** Contraction of a gamma matrix with something else. */
 146 bool diracgamma::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
 147 {
 148         GINAC_ASSERT(is_ex_of_type(*self, indexed));
 149         GINAC_ASSERT(is_ex_of_type(*other, indexed));
 150         GINAC_ASSERT(is_ex_of_type(self->op(0), diracgamma));
 151
 152         if (is_ex_of_type(other->op(0), diracgamma)) {
 153
 154                 ex dim = ex_to_idx(self->op(1)).get_dim();
 155
 156                 // gamma~mu*gamma.mu = dim*ONE
 157                 if (other - self == 1) {
 158                         *self = dim;
 159                         *other = dirac_ONE();
 160                         return true;
 161
 162                 // gamma~mu*gamma~alpha*gamma.mu = (2-dim)*gamma~alpha
 163                 } else if (other - self == 2
 164                         && is_ex_of_type(self[1], clifford)) {
 165                         *self = 2 - dim;
 166                         *other = _ex1();
 167                         return true;
 168
 169                 // gamma~mu*gamma~alpha*gamma~beta*gamma.mu = 4*g~alpha~beta+(dim-4)*gamam~alpha*gamma~beta
 170                 } else if (other - self == 3
 171                         && is_ex_of_type(self[1], clifford)
 172                         && is_ex_of_type(self[2], clifford)) {
 173                         *self = 4 * metric_tensor(self[1].op(1), self[2].op(1)) * dirac_ONE() + (dim - 4) * self[1] * self[2];
 174                         self[1] = _ex1();
 175                         self[2] = _ex1();
 176                         *other = _ex1();
 177                         return true;
 178
 179                 // gamma~mu*gamma~alpha*gamma~beta*gamma~delta*gamma.mu = -2*gamma~delta*gamma~beta*gamma~alpha+(4-dim)*gamma~alpha*gamma~beta*gamma~delta
 180                 } else if (other - self == 4
 181                         && is_ex_of_type(self[1], clifford)
 182                         && is_ex_of_type(self[2], clifford)
 183                         && is_ex_of_type(self[3], clifford)) {
 184                         *self = -2 * self[3] * self[2] * self[1] + (4 - dim) * self[1] * self[2] * self[3];
 185                         self[1] = _ex1();
 186                         self[2] = _ex1();
 187                         self[3] = _ex1();
 188                         *other = _ex1();
 189                         return true;
 190                 }
 191         }
 192
 193         return false;
 194 }
 195
 196 /** Perform automatic simplification on noncommutative product of clifford
 197  *  objects. This removes superfluous ONEs, permutes gamma5's to the front
 198  *  and removes squares of gamma objects. */
 199 ex clifford::simplify_ncmul(const exvector & v) const
 200 {
 201         exvector s;
 202         s.reserve(v.size());
 203
 204         // Remove superfluous ONEs
 205         exvector::const_iterator cit = v.begin(), citend = v.end();
 206         while (cit != citend) {
 207                 if (!is_ex_of_type(cit->op(0), diracone))
 208                         s.push_back(*cit);
 209                 cit++;
 210         }
 211
 212         bool something_changed = false;
 213         int sign = 1;
 214
 215         // Anticommute gamma5's to the front
 216         if (s.size() >= 2) {
 217                 exvector::iterator first = s.begin(), next_to_last = s.end() - 2;
 218                 while (true) {
 219                         exvector::iterator it = next_to_last;
 220                         while (true) {
 221                                 exvector::iterator it2 = it + 1;
 222                                 if (!is_ex_of_type(it->op(0), diracgamma5) && is_ex_of_type(it2->op(0), diracgamma5)) {
 223                                         it->swap(*it2);
 224                                         sign = -sign;
 225                                         something_changed = true;
 226                                 }
 227                                 if (it == first)
 228                                         break;
 229                                 it--;
 230                         }
 231                         if (next_to_last == first)
 232                                 break;
 233                         next_to_last--;
 234                 }
 235         }
 236
 237         // Remove squares of gamma5
 238         while (s.size() >= 2 && is_ex_of_type(s[0].op(0), diracgamma5) && is_ex_of_type(s[1].op(0), diracgamma5)) {
 239                 s.erase(s.begin(), s.begin() + 2);
 240                 something_changed = true;
 241         }
 242
 243         // Remove equal adjacent gammas
 244         if (s.size() >= 2) {
 245                 exvector::iterator it = s.begin(), itend = s.end() - 1;
 246                 while (it != itend) {
 247                         ex & a = it[0];
 248                         ex & b = it[1];
 249                         if (is_ex_of_type(a.op(0), diracgamma) && is_ex_of_type(b.op(0), diracgamma)) {
 250                                 const ex & ia = a.op(1);
 251                                 const ex & ib = b.op(1);
 252                                 if (ia.is_equal(ib)) {
 253                                         a = lorentz_g(ia, ib);
 254                                         b = dirac_ONE();
 255                                         something_changed = true;
 256                                 }
 257                         }
 258                         it++;
 259                 }
 260         }
 261
 262         if (s.size() == 0)
 263                 return clifford(diracone()) * sign;
 264         if (something_changed)
 265                 return nonsimplified_ncmul(s) * sign;
 266         else
 267                 return simplified_ncmul(s) * sign;
 268 }
 269
 270 ex clifford::thisexprseq(const exvector & v) const
 271 {
 272         return clifford(representation_label, v);
 273 }
 274
 275 ex clifford::thisexprseq(exvector * vp) const
 276 {
 277         return clifford(representation_label, vp);
 278 }
 279
 280 //////////
 281 // global functions
 282 //////////
 283
 284 ex dirac_ONE(unsigned char rl)
 285 {
 286         return clifford(diracone(), rl);
 287 }
 288
 289 ex dirac_gamma(const ex & mu, unsigned char rl)
 290 {
 291         if (!is_ex_of_type(mu, varidx))
 292                 throw(std::invalid_argument("index of Dirac gamma must be of type varidx"));
 293
 294         return clifford(diracgamma(), mu, rl);
 295 }
 296
 297 ex dirac_gamma5(unsigned char rl)
 298 {
 299         return clifford(diracgamma5(), rl);
 300 }
 301
 302 } // namespace GiNaC