88:, but with the generalisation of including a certain type of metric discontinuities: the face shared by two adjacent polyhedra has a unique area, but its shape can be different. This is a consequence of the quantum geometry of spin networks: ordinary Regge calculus is "too rigid" to account for all the geometric degrees of freedom described by the semiclassical limit of a spin network.
437:
25:
91:
The name twisted geometry captures the relation between these additional degrees of freedom and the off-shell presence of torsion in the theory, but also the fact that this classical description can be derived from
84:. A twisted geometry can be visualized as collections of polyhedra dual to the nodes of the spin network's graph. Intrinsic and extrinsic curvatures are defined in a manner similar to
502:
478:
96:, by assigning a pair of twistors to each link of the graph, and suitably constraining their helicities and incidence relations.
507:
497:
471:
378:
S. Speziale and
Wolfgang M. Wieland (2012). "The twistorial structure of loop-gravity transition amplitudes".
113:
L. Freidel and S. Speziale (2010). "Twisted geometries: A geometric parametrisation of SU(2) phase space".
464:
397:
344:
291:
238:
185:
132:
77:
413:
387:
360:
334:
307:
281:
254:
228:
201:
175:
148:
122:
444:
405:
352:
299:
246:
193:
140:
35:
219:
E. R. Livine and J. Tambornino (2012). "Spinor
Representation for Loop Quantum Gravity".
166:
C. Rovelli and S. Speziale (2010). "On the geometry of loop quantum gravity on a graph".
54:
401:
348:
295:
242:
189:
136:
448:
93:
85:
491:
364:
258:
205:
152:
81:
417:
311:
272:
E. Bianchi, P. Dona and S. Speziale (2011). "Polyhedra in loop quantum gravity".
409:
356:
303:
197:
144:
44:
24:
325:
L. Freidel and S. Speziale (2010). "From twistors to twisted geometries".
436:
250:
80:
and spin foam models, where they appear in the semiclassical limit of
392:
339:
286:
233:
180:
127:
18:
452:
49:
39:
472:
8:
76:are discrete geometries that play a role in
16:Discrete geometries used in spin foam models
479:
465:
391:
338:
285:
232:
179:
126:
105:
7:
433:
431:
14:
503:Physics beyond the Standard Model
435:
23:
1:
451:. You can help Knowledge by
524:
430:
410:10.1103/PhysRevD.86.124023
357:10.1103/PhysRevD.82.084041
304:10.1103/PhysRevD.83.044035
198:10.1103/PhysRevD.82.044018
145:10.1103/PhysRevD.82.084040
38:, as no other articles
447:-related article is a
508:Quantum physics stubs
498:Loop quantum gravity
78:loop quantum gravity
402:2012PhRvD..86l4023S
349:2010PhRvD..82h4041F
296:2011PhRvD..83d4035B
243:2012JMP....53a2503L
190:2010PhRvD..82d4018R
137:2010PhRvD..82h4040F
74:Twisted geometries
57:for suggestions.
47:to this page from
460:
459:
445:quantum mechanics
251:10.1063/1.3675465
71:
70:
515:
481:
474:
467:
439:
432:
422:
421:
395:
375:
369:
368:
342:
322:
316:
315:
289:
269:
263:
262:
236:
216:
210:
209:
183:
163:
157:
156:
130:
110:
66:
63:
52:
50:related articles
27:
19:
523:
522:
518:
517:
516:
514:
513:
512:
488:
487:
486:
485:
428:
426:
425:
377:
376:
372:
324:
323:
319:
271:
270:
266:
218:
217:
213:
165:
164:
160:
112:
111:
107:
102:
67:
61:
58:
48:
45:introduce links
28:
17:
12:
11:
5:
521:
519:
511:
510:
505:
500:
490:
489:
484:
483:
476:
469:
461:
458:
457:
440:
424:
423:
386:(12): 124023.
370:
317:
264:
211:
158:
104:
103:
101:
98:
94:Twistor theory
86:Regge calculus
69:
68:
55:Find link tool
31:
29:
22:
15:
13:
10:
9:
6:
4:
3:
2:
520:
509:
506:
504:
501:
499:
496:
495:
493:
482:
477:
475:
470:
468:
463:
462:
456:
454:
450:
446:
441:
438:
434:
429:
419:
415:
411:
407:
403:
399:
394:
389:
385:
381:
374:
371:
366:
362:
358:
354:
350:
346:
341:
336:
333:(8): 084041.
332:
328:
321:
318:
313:
309:
305:
301:
297:
293:
288:
283:
280:(4): 044035.
279:
275:
268:
265:
260:
256:
252:
248:
244:
240:
235:
230:
227:(1): 012503.
226:
222:
221:J. Math. Phys
215:
212:
207:
203:
199:
195:
191:
187:
182:
177:
174:(4): 044018.
173:
169:
162:
159:
154:
150:
146:
142:
138:
134:
129:
124:
121:(8): 084040.
120:
116:
109:
106:
99:
97:
95:
89:
87:
83:
82:spin networks
79:
75:
65:
62:December 2015
56:
51:
46:
42:
41:
37:
32:This article
30:
26:
21:
20:
453:expanding it
442:
427:
383:
380:Phys. Rev. D
379:
373:
330:
327:Phys. Rev. D
326:
320:
277:
274:Phys. Rev. D
273:
267:
224:
220:
214:
171:
168:Phys. Rev. D
167:
161:
118:
115:Phys. Rev. D
114:
108:
90:
73:
72:
59:
33:
492:Categories
100:References
53:; try the
40:link to it
393:1207.6348
365:119292655
340:1006.0199
287:1009.3402
259:119607941
234:1105.3385
206:118396168
181:1005.2927
153:119110824
128:1001.2748
43:. Please
418:59406729
312:14414561
398:Bibcode
345:Bibcode
292:Bibcode
239:Bibcode
186:Bibcode
133:Bibcode
416:
363:
310:
257:
204:
151:
36:orphan
34:is an
443:This
414:S2CID
388:arXiv
361:S2CID
335:arXiv
308:S2CID
282:arXiv
255:S2CID
229:arXiv
202:S2CID
176:arXiv
149:S2CID
123:arXiv
449:stub
406:doi
353:doi
300:doi
247:doi
194:doi
141:doi
494::
412:.
404:.
396:.
384:86
382:.
359:.
351:.
343:.
331:82
329:.
306:.
298:.
290:.
278:83
276:.
253:.
245:.
237:.
225:53
223:.
200:.
192:.
184:.
172:82
170:.
147:.
139:.
131:.
119:82
117:.
480:e
473:t
466:v
455:.
420:.
408::
400::
390::
367:.
355::
347::
337::
314:.
302::
294::
284::
261:.
249::
241::
231::
208:.
196::
188::
178::
155:.
143::
135::
125::
64:)
60:(
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
