Brisure de symétrie spontanée et géométrie du point de vue spectral
Séminaire Bourbaki (1995-1996)
- Volume: 38, page 313-349
- ISSN: 0303-1179
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topConnes, Alain. "Brisure de symétrie spontanée et géométrie du point de vue spectral." Séminaire Bourbaki 38 (1995-1996): 313-349. <http://eudml.org/doc/110219>.
@article{Connes1995-1996,
author = {Connes, Alain},
journal = {Séminaire Bourbaki},
keywords = {noncommutative geometry; infinitesimals; compact operators; trace; spectral triples; symmetry breaking; Fredholm index; Riemannian structures; spectral geometry; compact operators on graded Hilbert spaces},
language = {fre},
pages = {313-349},
publisher = {Société Mathématique de France},
title = {Brisure de symétrie spontanée et géométrie du point de vue spectral},
url = {http://eudml.org/doc/110219},
volume = {38},
year = {1995-1996},
}
TY - JOUR
AU - Connes, Alain
TI - Brisure de symétrie spontanée et géométrie du point de vue spectral
JO - Séminaire Bourbaki
PY - 1995-1996
PB - Société Mathématique de France
VL - 38
SP - 313
EP - 349
LA - fre
KW - noncommutative geometry; infinitesimals; compact operators; trace; spectral triples; symmetry breaking; Fredholm index; Riemannian structures; spectral geometry; compact operators on graded Hilbert spaces
UR - http://eudml.org/doc/110219
ER -
References
top- [At] M.F. Atiyah - K-theory and reality, Quart. J. Math. Oxford (2), 17 (1966), 367-386. Zbl0146.19101MR206940
- [B-G] R. Beals and P. Greiner - Calculus on Heisenberg manifolds, Annals of Math. Studies119, Princeton Univ. Press, Princeton, N.J., 1988. Zbl0654.58033MR953082
- [B] T.P. Branson - An anomaly associated with 4-dimensional quantum gravity, to appear in C.M.P. Zbl0864.53066
- [B-O] T.P. Branson and B. Ørsted - Explicit functional determinants in four dimensions, Proc. Amer. Math. Soc.113 (1991), 669-682. Zbl0762.47019MR1050018
- [B-W] A.R. Bernstein and F. Wattenberg - Non standard measure theory, in Applications of model theory to algebra analysis and probability, Edited by W.A.J. Luxenburg Halt, Rinehart and Winstin (1969). Zbl0195.01404
- [C-J-G] A.H. Chamseddine, J. Fröhlich and O. Grandjean - The gravitational sector in the Connes-Lott formulation of the Standard model, J. Math. Phys.36, n° 11 (1995). Zbl0846.58006MR1355907
- [C-C] A. Chamseddine and A. Connes - The spectral action principle, to appear. Zbl0894.58007MR1463819
- [Co] A. Connes - Noncommutative geometry, Academic Press (1994). Zbl0818.46076MR1303779
- [Co1] A. Connes - Cyclic cohomology and the transverse fundamental class of a foliation, Geometric methods in operator algebras, (Kyoto, 1983), pp. 52-144, Pitman Res. Notes in Math.123, Longman, Harlow (1986). Zbl0647.46054MR866491
- [Co2] A. Connes - Noncommutative geometry and reality, Journal of Math. Physics36, n° 11 (1995). Zbl0871.58008MR1355905
- [Co3] A. Connes - Gravity coupled with matter and the foundation of noncommutative geometry, to appear in C.M.P. Zbl0881.58009
- [Co-L] A. Connes and J. Lott - Particle models and noncommutative geometry, Nuclear Phys. B.18B (1990), suppl. 29-47 (1991). Zbl0957.46516MR1128127
- [C-M1] A. Connes and H. Moscovici - Cyclic cohomology, the Novikov conjecture and hyperbolic groups, Topology29 (1990), 345-388. Zbl0759.58047MR1066176
- [C-M2] A. Connes and H. Moscovici - The local index formula in noncommutative geometry, GAFA5 (1995), 174-243. Zbl0960.46048MR1334867
- [C-M3] A. Connes and H. Moscovici - Hypoelliptic Dirac operator, diffeomorphisms and the transverse fundamental class.
- [Co-S] A. Connes and G. Skandalis - The longitudinal index theorem for foliations, Publ. Res. Inst. Math. Sci. Kyoto20 (1984), 1139-1183. Zbl0575.58030MR775126
- [C-S-T] A. Connes, D. Sullivan and N. Teleman - Quasiconformal mappings, operators on Hilbert space, and local formulae for characteristic classes, Topology, Vol. 33, n° 4 (1994), 663-681. Zbl0840.57013MR1293305
- [D-T] T. Damour and J.H. Taylor - Strong field tests of relativistic gravity and binary pulsars, Physical Review D, Vol. 45, n° 6 (1992), 1840-1868.
- [Dx] J. Dixmier - Existence de traces non normales, C.R. Acad. Sci. Paris, Ser. A-B262 (1966). Zbl0141.12902MR196508
- [D-F-R] S. Doplicher, K. Fredenhagen and J.E. Roberts - Quantum structure of space time at the Planck scale and Quantum fields, to appear in CMP. Zbl0847.53051
- [F] J. Fröhlich - The noncommutative geometry of two dimensional supersymmetric conformal field theory, Preprint ETH (1994).
- [G-F] K. Gawedzki and J. Fröhlich - Conformal Field theory and Geometry of Strings, CRM Proceedings and Lecture Notes, Vol. 7 (1994), 57-97. Zbl0826.58007MR1311033
- [Gh] E. Ghys - L'invariant de Godbillon-Vey, Sém. Bourbaki1988/89, exposé 706, Astérisque177-178, S.M.F. (1989), 155-181. Zbl0707.57015MR1040572
- [Gi] P. Gilkey - Invariance theory, the heat equation and the Atiyah-Singer index theorem, Math. Lecture Ser.11, Publish or Perish, Wilmington, Del., 1984. Zbl0565.58035MR783634
- [G] M. Gromov - Carnot-Caratheodory spaces seen from within, Preprint IHES/ M/94/6. MR1421823
- [G-K-P] H. Grosse, C. Klimcik and P. Presnajder - On finite 4-dimensional quantum field theory in noncommutative geometry, CERN Preprint TH/96 - 51 Net Hepth/9602115.
- [H-S] M. Hilsum, G. Skandalis - Morphismes K-orientés d'espaces de feuilles et fonctorialité en théorie de Kasparov, Ann. Sci. Ecole Norm. Sup. (4) 20 (1987), 325-390. Zbl0656.57015MR925720
- [I-K-S] B. Iochum, D. Kastler and T. Schücker - Fuzzy mass relations for the Higgs, J.Math. Phys.36, n° 11 (1995). Zbl0848.46052MR1355906
- [K-W] W. Kalau and M. Walze - Gravity, noncommutative geometry and the Wodzicki residue, J. of Geom. and Phys.16 (1995), 327-344. Zbl0826.58008MR1336738
- [K] G. Kasparov - The operator K-functor and extensions of C*-algebras, Izv. Akad. Nauk. SSSR Ser. Mat.44 (1980), 571-636. Zbl0448.46051MR582160
- [Ka] C. Kassel - Le résidu non commutatif, Sém. Bourbaki1988/89, exposé 708, Astérisque177-178, S.M.F. (1989), 199-229. Zbl0701.58054MR1040574
- [Kas] D. Kastler - The Dirac operator and gravitation, Commun. Math. Phys.166 (1995), 633-643. Zbl0823.58046MR1312438
- [Ki] R.C. Kirby - Stable homeomorphisms and the annulus conjecture, Ann. Math.89 (1969), 575-582. Zbl0176.22004MR242165
- [L-M] B. Lawson and M.L. Michelson - Spin Geometry, Princeton1989. Zbl0688.57001
- [M] Y. Manin - Quantum groups and noncommutative geometry, Centre Recherche Math. Univ. Montréal (1988). Zbl0724.17006MR1016381
- [Mi-S] J. Milnor and D. Stasheff - Characteristic classes, Ann. of Math. Stud.76Princeton University Press, Princeton, N.J. (1974). Zbl0298.57008MR440554
- [P] S. Power - Hankel operators on Hilbert space, Res. Notes in Math.64, Pitman, Boston, Mass. (1982). Zbl0489.47011MR666699
- [Ri1] M.A. Rieffel - Morita equivalence for C*-algebras and W*-algebras, J. Pure Appl. Algebra5 (1974), 51-96. Zbl0295.46099MR367670
- [Ri2] M.A. Rieffel - C*-algebras associated with irrational rotations, Pacific J. Math.93 (1981), 415-429 ; MR 83b:46087. Zbl0499.46039MR623572
- [R] B. Riemann - Mathematical Werke, Dover, New York (1953). MR52364
- [St] E. Stein - Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton, N.J. (1970). Zbl0207.13501MR290095
- [Ste] J. Stern - Le problème de la mesure, Sém. Bourbaki1983/84, exposé 632, Astérisque121-122 (1985), 325-346. Zbl0632.28001MR768968
- [S1] D. Sullivan - Hyperbolic geometry and homeomorphisms in Geometric Topology, Proceed. Georgia Topology Conf. Athens, Georgia (1977), 543-555. Zbl0478.57007MR537749
- [S2] D. Sullivan - Geometric periodicity and the invariants of manifolds, Lecture Notes in Math.197, Springer (1971). Zbl0224.57002MR285012
- [Ta] M. Takesaki - Tomita's theory of modular Hilbert algebras and its applications, Lecture Notes in Math.128, Springer (1970). Zbl0193.42502MR270168
- [W] Weinberg - Gravitation and Cosmology, John Wiley and Sons, New YorkLondon (1972).
- [Wo] M. Wodzicki - Noncommutative residue, Part I. Fundamentals K-theory, arithmetic and geometry, Lecture Notes in Math., 1289, Springer-Berlin (1987). Zbl0649.58033MR923140
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