- color and clifford classes are quite functional now
[ginac.git] / 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 "symbol.h"
28 #include "print.h"
29 #include "archive.h"
30 #include "debugmsg.h"
31 #include "utils.h"
32
33 #include <stdexcept>
34
35 namespace GiNaC {
36
37 GINAC_IMPLEMENT_REGISTERED_CLASS(clifford, indexed)
38 GINAC_IMPLEMENT_REGISTERED_CLASS(diracone, tensor)
39 GINAC_IMPLEMENT_REGISTERED_CLASS(diracgamma, tensor)
40 GINAC_IMPLEMENT_REGISTERED_CLASS(diracgamma5, tensor)
41
42 //////////
43 // default constructor, destructor, copy constructor assignment operator and helpers
44 //////////
45
46 clifford::clifford() : representation_label(0)
47 {
48         debugmsg("clifford default constructor", LOGLEVEL_CONSTRUCT);
49         tinfo_key = TINFO_clifford;
50 }
51
52 void clifford::copy(const clifford & other)
53 {
54         inherited::copy(other);
55         representation_label = other.representation_label;
56 }
57
58 DEFAULT_DESTROY(clifford)
59 DEFAULT_CTORS(diracone)
60 DEFAULT_CTORS(diracgamma)
61 DEFAULT_CTORS(diracgamma5)
62
63 //////////
64 // other constructors
65 //////////
66
67 /** Construct object without any indices. This constructor is for internal
68  *  use only. Use the dirac_ONE() function instead.
69  *  @see dirac_ONE */
70 clifford::clifford(const ex & b, unsigned char rl) : inherited(b), representation_label(rl)
71 {
72         debugmsg("clifford constructor from ex", LOGLEVEL_CONSTRUCT);
73         tinfo_key = TINFO_clifford;
74 }
75
76 /** Construct object with one Lorentz index. This constructor is for internal
77  *  use only. Use the dirac_gamma() function instead.
78  *  @see dirac_gamma */
79 clifford::clifford(const ex & b, const ex & mu, unsigned char rl) : inherited(b, mu), representation_label(rl)
80 {
81         debugmsg("clifford constructor from ex,ex", LOGLEVEL_CONSTRUCT);
82         GINAC_ASSERT(is_ex_of_type(mu, varidx));
83         tinfo_key = TINFO_clifford;
84 }
85
86 clifford::clifford(unsigned char rl, const exvector & v, bool discardable) : inherited(indexed::unknown, v, discardable), representation_label(rl)
87 {
88         debugmsg("clifford constructor from unsigned char,exvector", LOGLEVEL_CONSTRUCT);
89         tinfo_key = TINFO_clifford;
90 }
91
92 clifford::clifford(unsigned char rl, exvector * vp) : inherited(indexed::unknown, vp), representation_label(rl)
93 {
94         debugmsg("clifford constructor from unsigned char,exvector *", LOGLEVEL_CONSTRUCT);
95         tinfo_key = TINFO_clifford;
96 }
97
98 //////////
99 // archiving
100 //////////
101
102 clifford::clifford(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
103 {
104         debugmsg("clifford constructor from archive_node", LOGLEVEL_CONSTRUCT);
105         unsigned rl;
106         n.find_unsigned("label", rl);
107         representation_label = rl;
108 }
109
110 void clifford::archive(archive_node &n) const
111 {
112         inherited::archive(n);
113         n.add_unsigned("label", representation_label);
114 }
115
116 DEFAULT_UNARCHIVE(clifford)
117 DEFAULT_ARCHIVING(diracone)
118 DEFAULT_ARCHIVING(diracgamma)
119 DEFAULT_ARCHIVING(diracgamma5)
120
121 //////////
122 // functions overriding virtual functions from bases classes
123 //////////
124
125 int clifford::compare_same_type(const basic & other) const
126 {
127         GINAC_ASSERT(other.tinfo() == TINFO_clifford);
128         const clifford &o = static_cast<const clifford &>(other);
129
130         if (representation_label != o.representation_label) {
131                 // different representation label
132                 return representation_label < o.representation_label ? -1 : 1;
133         }
134
135         return inherited::compare_same_type(other);
136 }
137
138 DEFAULT_COMPARE(diracone)
139 DEFAULT_COMPARE(diracgamma)
140 DEFAULT_COMPARE(diracgamma5)
141
142 DEFAULT_PRINT_LATEX(diracone, "ONE", "\\mathbb{1}")
143 DEFAULT_PRINT_LATEX(diracgamma, "gamma", "\\gamma")
144 DEFAULT_PRINT_LATEX(diracgamma5, "gamma5", "{\\gamma^5}")
145
146 /** Contraction of a gamma matrix with something else. */
147 bool diracgamma::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
148 {
149         GINAC_ASSERT(is_ex_of_type(*self, clifford));
150         GINAC_ASSERT(is_ex_of_type(*other, indexed));
151         GINAC_ASSERT(is_ex_of_type(self->op(0), diracgamma));
152         unsigned char rl = ex_to_clifford(*self).get_representation_label();
153
154         if (is_ex_of_type(*other, clifford)) {
155
156                 ex dim = ex_to_idx(self->op(1)).get_dim();
157
158                 // gamma~mu gamma.mu = dim ONE
159                 if (other - self == 1) {
160                         *self = dim;
161                         *other = dirac_ONE(rl);
162                         return true;
163
164                 // gamma~mu gamma~alpha gamma.mu = (2-dim) gamma~alpha
165                 } else if (other - self == 2
166                         && is_ex_of_type(self[1], clifford)) {
167                         *self = 2 - dim;
168                         *other = _ex1();
169                         return true;
170
171                 // gamma~mu gamma~alpha gamma~beta gamma.mu = 4 g~alpha~beta + (dim-4) gamam~alpha gamma~beta
172                 } else if (other - self == 3
173                         && is_ex_of_type(self[1], clifford)
174                         && is_ex_of_type(self[2], clifford)) {
175                         *self = 4 * lorentz_g(self[1].op(1), self[2].op(1)) * dirac_ONE(rl) + (dim - 4) * self[1] * self[2];
176                         self[1] = _ex1();
177                         self[2] = _ex1();
178                         *other = _ex1();
179                         return true;
180
181                 // gamma~mu S gamma~alpha gamma.mu = 2 gamma~alpha S - gamma~mu S gamma.mu gamma~alpha
182                 // (commutate contracted indices towards each other, simplify_indexed()
183                 // will re-expand and re-run the simplification)
184                 } else {
185                         exvector::iterator it = self + 1, next_to_last = other - 1;
186                         while (it != other) {
187                                 if (!is_ex_of_type(*it, clifford))
188                                         return false;
189                                 it++;
190                         }
191
192                         it = self + 1;
193                         ex S = _ex1();
194                         while (it != next_to_last) {
195                                 S *= *it;
196                                 *it++ = _ex1();
197                         }
198
199                         *self = 2 * (*next_to_last) * S - (*self) * S * (*other) * (*next_to_last);
200                         *next_to_last = _ex1();
201                         *other = _ex1();
202                         return true;
203                 }
204         }
205
206         return false;
207 }
208
209 /** Perform automatic simplification on noncommutative product of clifford
210  *  objects. This removes superfluous ONEs, permutes gamma5's to the front
211  *  and removes squares of gamma objects. */
212 ex clifford::simplify_ncmul(const exvector & v) const
213 {
214         exvector s;
215         s.reserve(v.size());
216         unsigned rl = ex_to_clifford(v[0]).get_representation_label();
217
218         // Remove superfluous ONEs
219         exvector::const_iterator cit = v.begin(), citend = v.end();
220         while (cit != citend) {
221                 if (!is_ex_of_type(cit->op(0), diracone))
222                         s.push_back(*cit);
223                 cit++;
224         }
225
226         bool something_changed = false;
227         int sign = 1;
228
229         // Anticommute gamma5's to the front
230         if (s.size() >= 2) {
231                 exvector::iterator first = s.begin(), next_to_last = s.end() - 2;
232                 while (true) {
233                         exvector::iterator it = next_to_last;
234                         while (true) {
235                                 exvector::iterator it2 = it + 1;
236                                 if (!is_ex_of_type(it->op(0), diracgamma5) && is_ex_of_type(it2->op(0), diracgamma5)) {
237                                         it->swap(*it2);
238                                         sign = -sign;
239                                         something_changed = true;
240                                 }
241                                 if (it == first)
242                                         break;
243                                 it--;
244                         }
245                         if (next_to_last == first)
246                                 break;
247                         next_to_last--;
248                 }
249         }
250
251         // Remove squares of gamma5
252         while (s.size() >= 2 && is_ex_of_type(s[0].op(0), diracgamma5) && is_ex_of_type(s[1].op(0), diracgamma5)) {
253                 s.erase(s.begin(), s.begin() + 2);
254                 something_changed = true;
255         }
256
257         // Remove equal adjacent gammas
258         if (s.size() >= 2) {
259                 exvector::iterator it = s.begin(), itend = s.end() - 1;
260                 while (it != itend) {
261                         ex & a = it[0];
262                         ex & b = it[1];
263                         if (is_ex_of_type(a.op(0), diracgamma) && is_ex_of_type(b.op(0), diracgamma)) {
264                                 const ex & ia = a.op(1);
265                                 const ex & ib = b.op(1);
266                                 if (ia.is_equal(ib)) {
267                                         a = lorentz_g(ia, ib);
268                                         b = dirac_ONE(rl);
269                                         something_changed = true;
270                                 }
271                         }
272                         it++;
273                 }
274         }
275
276         if (s.size() == 0)
277                 return clifford(diracone(), rl) * sign;
278         if (something_changed)
279                 return nonsimplified_ncmul(s) * sign;
280         else
281                 return simplified_ncmul(s) * sign;
282 }
283
284 ex clifford::thisexprseq(const exvector & v) const
285 {
286         return clifford(representation_label, v);
287 }
288
289 ex clifford::thisexprseq(exvector * vp) const
290 {
291         return clifford(representation_label, vp);
292 }
293
294 //////////
295 // global functions
296 //////////
297
298 ex dirac_ONE(unsigned char rl)
299 {
300         return clifford(diracone(), rl);
301 }
302
303 ex dirac_gamma(const ex & mu, unsigned char rl)
304 {
305         if (!is_ex_of_type(mu, varidx))
306                 throw(std::invalid_argument("index of Dirac gamma must be of type varidx"));
307
308         return clifford(diracgamma(), mu, rl);
309 }
310
311 ex dirac_gamma5(unsigned char rl)
312 {
313         return clifford(diracgamma5(), rl);
314 }
315
316 ex dirac_gamma6(unsigned char rl)
317 {
318         return clifford(diracone(), rl) + clifford(diracgamma5(), rl);
319 }
320
321 ex dirac_gamma7(unsigned char rl)
322 {
323         return clifford(diracone(), rl) - clifford(diracgamma5(), rl);
324 }
325
326 ex dirac_slash(const ex & e, const ex & dim, unsigned char rl)
327 {
328         varidx mu((new symbol)->setflag(status_flags::dynallocated), dim);
329         return indexed(e, mu.toggle_variance()) * dirac_gamma(mu, rl);
330 }
331
332 /** Check whether a given tinfo key (as returned by return_type_tinfo()
333  *  is that of a clifford object with the specified representation label. */
334 static bool is_clifford_tinfo(unsigned ti, unsigned char rl)
335 {
336         return ti == (TINFO_clifford + rl);
337 }
338
339 ex dirac_trace(const ex & e, unsigned char rl)
340 {
341         if (is_ex_of_type(e, clifford)) {
342
343                 if (ex_to_clifford(e).get_representation_label() == rl
344                  && is_ex_of_type(e.op(0), diracone))
345                         return _ex4();
346                 else
347                         return _ex0();
348
349         } else if (is_ex_exactly_of_type(e, add)) {
350
351                 // Trace of sum = sum of traces
352                 ex sum = _ex0();
353                 for (unsigned i=0; i<e.nops(); i++)
354                         sum += dirac_trace(e.op(i), rl);
355                 return sum;
356
357         } else if (is_ex_exactly_of_type(e, mul)) {
358
359                 // Trace of product: pull out non-clifford factors
360                 ex prod = _ex1();
361                 for (unsigned i=0; i<e.nops(); i++) {
362                         const ex &o = e.op(i);
363                         unsigned ti = o.return_type_tinfo();
364                         if (is_clifford_tinfo(o.return_type_tinfo(), rl))
365                                 prod *= dirac_trace(o, rl);
366                         else
367                                 prod *= o;
368                 }
369                 return prod;
370
371         } else if (is_ex_exactly_of_type(e, ncmul)) {
372
373                 if (!is_clifford_tinfo(e.return_type_tinfo(), rl))
374                         return _ex0();
375
376                 // Expand product, if necessary
377                 ex e_expanded = e.expand();
378                 if (!is_ex_of_type(e_expanded, ncmul))
379                         return dirac_trace(e_expanded, rl);
380
381                 // gamma5 gets moved to the front so this check is enough
382                 bool has_gamma5 = is_ex_of_type(e.op(0).op(0), diracgamma5);
383                 unsigned num = e.nops();
384
385                 if (has_gamma5) {
386
387                         // Trace of gamma5 * odd number of gammas and trace of
388                         // gamma5 * gamma.mu * gamma.nu are zero
389                         if ((num & 1) == 0 || num == 3)
390                                 return _ex0();
391
392                         // Tr gamma5 S_2k =
393                         //   epsilon0123.mu1.mu2.mu3.mu4 * Tr gamma.mu1 gamma.mu2 gamma.mu3 gamma.mu4 S_2k
394                         ex dim = ex_to_idx(e.op(1).op(1)).get_dim();
395                         varidx mu1((new symbol)->setflag(status_flags::dynallocated), dim),
396                                mu2((new symbol)->setflag(status_flags::dynallocated), dim),
397                                mu3((new symbol)->setflag(status_flags::dynallocated), dim),
398                                mu4((new symbol)->setflag(status_flags::dynallocated), dim);
399                         exvector v;
400                         v.reserve(num + 3);
401                         v.push_back(dirac_gamma(mu1, rl));
402                         v.push_back(dirac_gamma(mu2, rl));
403                         v.push_back(dirac_gamma(mu3, rl));
404                         v.push_back(dirac_gamma(mu4, rl));
405                         for (int i=1; i<num; i++)
406                                 v.push_back(e.op(i));
407
408                         return (eps0123(mu1.toggle_variance(), mu2.toggle_variance(), mu3.toggle_variance(), mu4.toggle_variance()) *
409                                 dirac_trace(ncmul(v), rl)).simplify_indexed() / 24;
410
411                 } else { // no gamma5
412
413                         // Trace of odd number of gammas is zero
414                         if ((num & 1) == 1)
415                                 return _ex0();
416
417                         // Tr gamma.mu gamma.nu = 4 g.mu.nu
418                         if (num == 2)
419                                 return 4 * lorentz_g(e.op(0).op(1), e.op(1).op(1));
420
421                         // Traces of 4 or more gammas are computed recursively:
422                         // Tr gamma.mu1 gamma.mu2 ... gamma.mun =
423                         //   + g.mu1.mu2 * Tr gamma.mu3 ... gamma.mun
424                         //   - g.mu1.mu3 * Tr gamma.mu2 gamma.mu4 ... gamma.mun
425                         //   + g.mu1.mu4 * Tr gamma.mu3 gamma.mu3 gamma.mu5 ... gamma.mun
426                         //   - ...
427                         //   + g.mu1.mun * Tr gamma.mu2 ... gamma.mu(n-1)
428                         exvector v(num - 2);
429                         int sign = 1;
430                         const ex &ix1 = e.op(0).op(1);
431                         ex result;
432                         for (int i=1; i<num; i++) {
433                                 for (int n=1, j=0; n<num; n++) {
434                                         if (n == i)
435                                                 continue;
436                                         v[j++] = e.op(n);
437                                 }
438                                 result += sign * lorentz_g(ix1, e.op(i).op(1)) * dirac_trace(ncmul(v), rl);
439                                 sign = -sign;
440                         }
441                         return result;
442                 }
443         }
444
445         return _ex0();
446 }
447
448 } // namespace GiNaC