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 "archive.h"
  28 #include "debugmsg.h"
  29 #include "utils.h"
  30
  31 #include <stdexcept>
  32
  33 namespace GiNaC {
  34
  35 GINAC_IMPLEMENT_REGISTERED_CLASS(clifford, indexed)
  36 GINAC_IMPLEMENT_REGISTERED_CLASS(diracone, tensor)
  37 GINAC_IMPLEMENT_REGISTERED_CLASS(diracgamma, tensor)
  38
  39 //////////
  40 // default constructor, destructor, copy constructor assignment operator and helpers
  41 //////////
  42
  43 clifford::clifford()
  44 {
  45         debugmsg("clifford default constructor", LOGLEVEL_CONSTRUCT);
  46         tinfo_key = TINFO_clifford;
  47 }
  48
  49 DEFAULT_COPY(clifford)
  50 DEFAULT_DESTROY(clifford)
  51 DEFAULT_CTORS(diracone)
  52 DEFAULT_CTORS(diracgamma)
  53
  54 //////////
  55 // other constructors
  56 //////////
  57
  58 /** Construct object with one Lorentz index. This constructor is for internal
  59  *  use only. Use the dirac_gamma() function instead.
  60  *  @see dirac_gamma */
  61 clifford::clifford(const ex & b, const ex & mu) : inherited(b, mu)
  62 {
  63         debugmsg("clifford constructor from ex,ex", LOGLEVEL_CONSTRUCT);
  64         GINAC_ASSERT(is_ex_of_type(mu, varidx));
  65         tinfo_key = TINFO_clifford;
  66 }
  67
  68 /** Construct object without any indices. This constructor is for internal
  69  *  use only. Use the dirac_one() function instead.
  70  *  @see dirac_one */
  71 clifford::clifford(const ex & b) : inherited(b)
  72 {
  73         debugmsg("clifford constructor from ex", LOGLEVEL_CONSTRUCT);
  74         tinfo_key = TINFO_clifford;
  75 }
  76
  77 clifford::clifford(const exvector & v, bool discardable) : inherited(indexed::unknown, v, discardable)
  78 {
  79         debugmsg("clifford constructor from exvector", LOGLEVEL_CONSTRUCT);
  80         tinfo_key = TINFO_clifford;
  81 }
  82
  83 clifford::clifford(exvector * vp) : inherited(indexed::unknown, vp)
  84 {
  85         debugmsg("clifford constructor from exvector *", LOGLEVEL_CONSTRUCT);
  86         tinfo_key = TINFO_clifford;
  87 }
  88
  89 //////////
  90 // archiving
  91 //////////
  92
  93 DEFAULT_ARCHIVING(clifford)
  94 DEFAULT_ARCHIVING(diracone)
  95 DEFAULT_ARCHIVING(diracgamma)
  96
  97 //////////
  98 // functions overriding virtual functions from bases classes
  99 //////////
 100
 101 int clifford::compare_same_type(const basic & other) const
 102 {
 103         return inherited::compare_same_type(other);
 104 }
 105
 106 DEFAULT_COMPARE(diracone)
 107 DEFAULT_COMPARE(diracgamma)
 108 DEFAULT_PRINT(diracone, "ONE")
 109 DEFAULT_PRINT(diracgamma, "gamma")
 110
 111 /** Contraction of a gamma matrix with something else. */
 112 bool diracgamma::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
 113 {
 114         GINAC_ASSERT(is_ex_of_type(*self, indexed));
 115         GINAC_ASSERT(is_ex_of_type(*other, indexed));
 116         GINAC_ASSERT(is_ex_of_type(self->op(0), diracgamma));
 117
 118         if (is_ex_of_type(other->op(0), diracgamma)) {
 119
 120                 ex dim = ex_to_idx(self->op(1)).get_dim();
 121
 122                 // gamma~mu*gamma.mu = dim*ONE
 123                 if (other - self == 1) {
 124                         *self = dim;
 125                         *other = dirac_one();
 126                         return true;
 127
 128                 // gamma~mu*gamma~alpha*gamma.mu = (2-dim)*gamma~alpha
 129                 } else if (other - self == 2
 130                         && is_ex_of_type(self[1], clifford)) {
 131                         *self = 2 - dim;
 132                         *other = _ex1();
 133                         return true;
 134
 135                 // gamma~mu*gamma~alpha*gamma~beta*gamma.mu = 4*g~alpha~beta+(dim-4)*gamam~alpha*gamma~beta
 136                 } else if (other - self == 3
 137                         && is_ex_of_type(self[1], clifford)
 138                         && is_ex_of_type(self[2], clifford)) {
 139                         *self = 4 * metric_tensor(self[1].op(1), self[2].op(1)) * dirac_one() + (dim - 4) * self[1] * self[2];
 140                         self[1] = _ex1();
 141                         self[2] = _ex1();
 142                         *other = _ex1();
 143                         return true;
 144
 145                 // 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
 146                 } else if (other - self == 4
 147                         && is_ex_of_type(self[1], clifford)
 148                         && is_ex_of_type(self[2], clifford)
 149                         && is_ex_of_type(self[3], clifford)) {
 150                         *self = -2 * self[3] * self[2] * self[1] + (4 - dim) * self[1] * self[2] * self[3];
 151                         self[1] = _ex1();
 152                         self[2] = _ex1();
 153                         self[3] = _ex1();
 154                         *other = _ex1();
 155                         return true;
 156                 }
 157         }
 158
 159         return false;
 160 }
 161
 162 /** Perform automatic simplification on noncommutative product of clifford
 163  *  objects. This removes superfluous ONEs. */
 164 ex clifford::simplify_ncmul(const exvector & v) const
 165 {
 166         exvector s;
 167         s.reserve(v.size());
 168
 169         exvector::const_iterator it = v.begin(), itend = v.end();
 170         while (it != itend) {
 171                 if (!is_ex_of_type(it->op(0), diracone))
 172                         s.push_back(*it);
 173                 it++;
 174         }
 175
 176         if (s.size() == 0)
 177                 return clifford(diracone());
 178         else if (s.size() == v.size())
 179                 return simplified_ncmul(v);
 180         else
 181                 return simplified_ncmul(s);
 182 }
 183
 184 ex clifford::thisexprseq(const exvector & v) const
 185 {
 186         return clifford(v);
 187 }
 188
 189 ex clifford::thisexprseq(exvector * vp) const
 190 {
 191         return clifford(vp);
 192 }
 193
 194 //////////
 195 // global functions
 196 //////////
 197
 198 ex dirac_one(void)
 199 {
 200         return clifford(diracone());
 201 }
 202
 203 ex dirac_gamma(const ex & mu)
 204 {
 205         if (!is_ex_of_type(mu, varidx))
 206                 throw(std::invalid_argument("index of Dirac gamma must be of type varidx"));
 207
 208         return clifford(diracgamma(), mu);
 209 }
 210
 211 } // namespace GiNaC