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
  40 //////////
  41 // default constructor, destructor, copy constructor assignment operator and helpers
  42 //////////
  43
  44 clifford::clifford()
  45 {
  46         debugmsg("clifford default constructor", LOGLEVEL_CONSTRUCT);
  47         tinfo_key = TINFO_clifford;
  48 }
  49
  50 DEFAULT_COPY(clifford)
  51 DEFAULT_DESTROY(clifford)
  52 DEFAULT_CTORS(diracone)
  53 DEFAULT_CTORS(diracgamma)
  54
  55 //////////
  56 // other constructors
  57 //////////
  58
  59 /** Construct object with one Lorentz index. This constructor is for internal
  60  *  use only. Use the dirac_gamma() function instead.
  61  *  @see dirac_gamma */
  62 clifford::clifford(const ex & b, const ex & mu) : inherited(b, mu)
  63 {
  64         debugmsg("clifford constructor from ex,ex", LOGLEVEL_CONSTRUCT);
  65         GINAC_ASSERT(is_ex_of_type(mu, varidx));
  66         tinfo_key = TINFO_clifford;
  67 }
  68
  69 /** Construct object without any indices. This constructor is for internal
  70  *  use only. Use the dirac_one() function instead.
  71  *  @see dirac_one */
  72 clifford::clifford(const ex & b) : inherited(b)
  73 {
  74         debugmsg("clifford constructor from ex", LOGLEVEL_CONSTRUCT);
  75         tinfo_key = TINFO_clifford;
  76 }
  77
  78 clifford::clifford(const exvector & v, bool discardable) : inherited(indexed::unknown, v, discardable)
  79 {
  80         debugmsg("clifford constructor from exvector", LOGLEVEL_CONSTRUCT);
  81         tinfo_key = TINFO_clifford;
  82 }
  83
  84 clifford::clifford(exvector * vp) : inherited(indexed::unknown, vp)
  85 {
  86         debugmsg("clifford constructor from exvector *", LOGLEVEL_CONSTRUCT);
  87         tinfo_key = TINFO_clifford;
  88 }
  89
  90 //////////
  91 // archiving
  92 //////////
  93
  94 DEFAULT_ARCHIVING(clifford)
  95 DEFAULT_ARCHIVING(diracone)
  96 DEFAULT_ARCHIVING(diracgamma)
  97
  98 //////////
  99 // functions overriding virtual functions from bases classes
 100 //////////
 101
 102 int clifford::compare_same_type(const basic & other) const
 103 {
 104         return inherited::compare_same_type(other);
 105 }
 106
 107 DEFAULT_COMPARE(diracone)
 108 DEFAULT_COMPARE(diracgamma)
 109 DEFAULT_PRINT(diracone, "ONE")
 110 DEFAULT_PRINT(diracgamma, "gamma")
 111
 112 /** Contraction of a gamma matrix with something else. */
 113 bool diracgamma::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
 114 {
 115         GINAC_ASSERT(is_ex_of_type(*self, indexed));
 116         GINAC_ASSERT(is_ex_of_type(*other, indexed));
 117         GINAC_ASSERT(is_ex_of_type(self->op(0), diracgamma));
 118
 119         if (is_ex_of_type(other->op(0), diracgamma)) {
 120
 121                 ex dim = ex_to_idx(self->op(1)).get_dim();
 122
 123                 // gamma~mu*gamma.mu = dim*ONE
 124                 if (other - self == 1) {
 125                         *self = dim;
 126                         *other = dirac_one();
 127                         return true;
 128
 129                 // gamma~mu*gamma~alpha*gamma.mu = (2-dim)*gamma~alpha
 130                 } else if (other - self == 2
 131                         && is_ex_of_type(self[1], clifford)) {
 132                         *self = 2 - dim;
 133                         *other = _ex1();
 134                         return true;
 135
 136                 // gamma~mu*gamma~alpha*gamma~beta*gamma.mu = 4*g~alpha~beta+(dim-4)*gamam~alpha*gamma~beta
 137                 } else if (other - self == 3
 138                         && is_ex_of_type(self[1], clifford)
 139                         && is_ex_of_type(self[2], clifford)) {
 140                         *self = 4 * metric_tensor(self[1].op(1), self[2].op(1)) * dirac_one() + (dim - 4) * self[1] * self[2];
 141                         self[1] = _ex1();
 142                         self[2] = _ex1();
 143                         *other = _ex1();
 144                         return true;
 145
 146                 // 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
 147                 } else if (other - self == 4
 148                         && is_ex_of_type(self[1], clifford)
 149                         && is_ex_of_type(self[2], clifford)
 150                         && is_ex_of_type(self[3], clifford)) {
 151                         *self = -2 * self[3] * self[2] * self[1] + (4 - dim) * self[1] * self[2] * self[3];
 152                         self[1] = _ex1();
 153                         self[2] = _ex1();
 154                         self[3] = _ex1();
 155                         *other = _ex1();
 156                         return true;
 157                 }
 158         }
 159
 160         return false;
 161 }
 162
 163 /** Perform automatic simplification on noncommutative product of clifford
 164  *  objects. This removes superfluous ONEs. */
 165 ex clifford::simplify_ncmul(const exvector & v) const
 166 {
 167         exvector s;
 168         s.reserve(v.size());
 169
 170         exvector::const_iterator it = v.begin(), itend = v.end();
 171         while (it != itend) {
 172                 if (!is_ex_of_type(it->op(0), diracone))
 173                         s.push_back(*it);
 174                 it++;
 175         }
 176
 177         if (s.size() == 0)
 178                 return clifford(diracone());
 179         else if (s.size() == v.size())
 180                 return simplified_ncmul(v);
 181         else
 182                 return simplified_ncmul(s);
 183 }
 184
 185 ex clifford::thisexprseq(const exvector & v) const
 186 {
 187         return clifford(v);
 188 }
 189
 190 ex clifford::thisexprseq(exvector * vp) const
 191 {
 192         return clifford(vp);
 193 }
 194
 195 //////////
 196 // global functions
 197 //////////
 198
 199 ex dirac_one(void)
 200 {
 201         return clifford(diracone());
 202 }
 203
 204 ex dirac_gamma(const ex & mu)
 205 {
 206         if (!is_ex_of_type(mu, varidx))
 207                 throw(std::invalid_argument("index of Dirac gamma must be of type varidx"));
 208
 209         return clifford(diracgamma(), mu);
 210 }
 211
 212 } // namespace GiNaC