@article{BSMF_1964__92__11_0, author = {Lichnerowicz, Andr\'e}, title = {Champs spinoriels et propagateurs en relativit\'e g\'en\'erale}, journal = {Bulletin de la Soci\'et\'e Math\'ematique de France}, pages = {11--100}, publisher = {Soci\'et\'e math\'ematique de France}, volume = {92}, year = {1964}, doi = {10.24033/bsmf.1604}, mrnumber = {29 #6913}, zbl = {0138.44301}, language = {fr}, url = {https://numdam.org/articles/10.24033/bsmf.1604/} }
TY - JOUR AU - Lichnerowicz, André TI - Champs spinoriels et propagateurs en relativité générale JO - Bulletin de la Société Mathématique de France PY - 1964 SP - 11 EP - 100 VL - 92 PB - Société mathématique de France UR - https://numdam.org/articles/10.24033/bsmf.1604/ DO - 10.24033/bsmf.1604 LA - fr ID - BSMF_1964__92__11_0 ER -
%0 Journal Article %A Lichnerowicz, André %T Champs spinoriels et propagateurs en relativité générale %J Bulletin de la Société Mathématique de France %D 1964 %P 11-100 %V 92 %I Société mathématique de France %U https://numdam.org/articles/10.24033/bsmf.1604/ %R 10.24033/bsmf.1604 %G fr %F BSMF_1964__92__11_0
Lichnerowicz, André. Champs spinoriels et propagateurs en relativité générale. Bulletin de la Société Mathématique de France, Tome 92 (1964), pp. 11-100. doi : 10.24033/bsmf.1604. https://numdam.org/articles/10.24033/bsmf.1604/
[1] Introduction à la théorie quantique des champs. - Paris, Dunod, 1960 (Travaux et Recherches mathématiques, 5).
et . -[2] Propagateurs et solutions d'équations homogènes hyperboliques, C. R. Acad. Sc. Paris, t. 251, 1960, p. 29-31. | Zbl
. -[3] Théorie générale des particules à spin, 2e édition. - Paris, Gauthier-Villars, 1954. | Zbl
. -[4] On the characteristic matrices of covariant systems, Phys. Rev., t. 54, 1938, p. 1114. | JFM | Zbl
. -[5] Sur l'extension du groupe structural d'un espace fibré, C. R. Acad. Sc. Paris, t. 243, 1956, p. 558-560. | Zbl
. -[6] Introduction à l'électrodynamique quantique. - Paris, Dunod, 1961 (Travaux et Recherches mathématiques, 6). | Zbl
. -[7] The particle aspect of meson theory, Proc. Royal Soc., Series A, t. 173, 1939, p. 91-116. | JFM | MR | Zbl
. -[8] Hyperbolic differential equations. - Princeton, Princeton University Press, 1952 (multigraphié).
. -[9] Propagateurs et commutateurs en relativité générale. - Paris, Presses universitaires de France, 1961 (Institut des hautes Études scientifiques, Publications mathématiques, 10). | Numdam | Zbl
. -[10] Propagateurs antisymétriques en relativité générale, Quantification du champ électromagnétique dans le vide, C. R. Acad. Sc. Paris, t. 249, 1959, p. 1329-1331 ; Sur la quantification du champ de gravitation pour un espace-temps à courbure constante, C. R. Acad. Sc. Paris, t. 249, 1959, p. 2287-2289 ; Sur la quantification du champ de gravitation, C. R. Acad. Sc. Paris, t. 250, 1960, p. 3122-3124. | Zbl
. -[11] Anticommutateur du champ spinoriel en relativité générale, C. R. Acad. Sc. Paris, t. 252, 1961, p. 3742-3744 ; Sur la quantification du champ correspondant au spin 3/2 sur un espace d'Einstein, C. R. Acad. Sc. Paris, t. 253, 1961, p. 940-942 ; Théorie de Petiau-Duffin-Kemmer en relativité générale, C. R. Acad. Sc. Paris, t. 253, 1961, p. 983-985. | Zbl
. -[12] Les spineurs en relativité générale, Seminario di Matematica, Bari, 1962. | Zbl
. -[13] Laplacien et spineurs, Att. Accad. naz. dei Lincei, Rendiconti, t. 33, fasc. 5, 1962.
. -[14] Contribution à l'étude des équations d'ondes corpusculaires, Acad. royale Belg., Cl. Sc. math., Mémoires, 2e série, t. 16, n° 2, 118 pages (Thèse Sc. math., Paris, 1936). | JFM
. -[15] On a theory of particles with half-integral spin, Phys. Rev., t. 60, 1941, p. 61. | Zbl
and . -[16] The general theory of the interaction representation, I., Progress theor. Phys., t. 9, 1953, p. 14-32. | MR | Zbl
and . -[17] Théorie quantique des champs, Tome 1. - Paris, Gauthier-Villars, 1961 (Traité de Physique théorique et de Physique mathématique, 14). | Zbl
. -- Huygens' principle for the Dirac equation in spacetime of non-constant curvature, Journal of Mathematical Analysis and Applications, Volume 517 (2023) no. 1, p. 126614 | DOI:10.1016/j.jmaa.2022.126614
- Huygens’ principle for the generalized Dirac operator in curved spacetime, Journal of Physics A: Mathematical and Theoretical, Volume 54 (2021) no. 9, p. 095204 | DOI:10.1088/1751-8121/abdde9
- Obstruction Class for the Existence of a Conformal Spin Structure in a Strict Sense, Advances in Applied Clifford Algebras, Volume 30 (2020) no. 2 | DOI:10.1007/s00006-020-1044-2
- Field equations from Killing spinors, Journal of Mathematical Physics, Volume 59 (2018) no. 2 | DOI:10.1063/1.4989434
- A Few Comments on Conformal Spin Structures and Conformal U(1)-Spin Structures on a Pseudo-Riemannian 2r-Dimensional Manifold V, Advances in Applied Clifford Algebras, Volume 27 (2017) no. 1, p. 165 | DOI:10.1007/s00006-016-0648-z
- Spin precession of Dirac particles in Kerr geometry, Classical and Quantum Gravity, Volume 34 (2017) no. 2, p. 025001 | DOI:10.1088/1361-6382/34/2/025001
- Dark matter and localised fermions from spherical orbifolds?, Journal of High Energy Physics, Volume 2016 (2016) no. 4, p. 1 | DOI:10.1007/jhep04(2016)083
- Higher-degree Dirac currents of twistor and Killing spinors in supergravity theories, Classical and Quantum Gravity, Volume 32 (2015) no. 17, p. 175007 | DOI:10.1088/0264-9381/32/17/175007
- Compatibility of symmetric quantization with general covariance in the Dirac equation and spin connections, Physics Letters A, Volume 379 (2015) no. 45-46, p. 2946 | DOI:10.1016/j.physleta.2015.08.021
- Dirac operator on spinors and diffeomorphisms, Classical and Quantum Gravity, Volume 30 (2013) no. 1, p. 015006 | DOI:10.1088/0264-9381/30/1/015006
- Bending and flexural phonon scattering: Generalized Dirac equation for an electron moving in curved graphene, Physica B: Condensed Matter, Volume 407 (2012) no. 12, p. 2002 | DOI:10.1016/j.physb.2012.01.129
- A solution of the non‐uniqueness problem of the Dirac Hamiltonian and energy operators, Annalen der Physik, Volume 523 (2011) no. 12, p. 1008 | DOI:10.1002/andp.201100166
- Positive gravitational energy in arbitrary dimensions, Comptes Rendus. Mathématique, Volume 349 (2011) no. 15-16, p. 915 | DOI:10.1016/j.crma.2011.07.017
- The universal extra dimensional model with S2/Z2 extra-space, Nuclear Physics B, Volume 830 (2010) no. 3, p. 414 | DOI:10.1016/j.nuclphysb.2009.11.023
- Detours and paths: BRST complexes and worldline formalism, Journal of High Energy Physics, Volume 2009 (2009) no. 05, p. 017 | DOI:10.1088/1126-6708/2009/05/017
- Surgery and bordism groups in quantum partial differential equations. I: The quantum Poincaré conjecture, Nonlinear Analysis: Theory, Methods Applications, Volume 71 (2009) no. 12, p. e502 | DOI:10.1016/j.na.2008.11.077
- Surgery and bordism groups in quantum partial differential equations, II: Variational quantum PDEs, Nonlinear Analysis: Theory, Methods Applications, Volume 71 (2009) no. 12, p. e526 | DOI:10.1016/j.na.2008.10.063
- Tractors, mass, and Weyl invariance, Nuclear Physics B, Volume 812 (2009) no. 3, p. 424 | DOI:10.1016/j.nuclphysb.2008.11.026
- (p,q)-form Kähler electromagnetism, Physics Letters B, Volume 674 (2009) no. 4-5, p. 316 | DOI:10.1016/j.physletb.2009.03.046
- Classic Groups: Clifford Algebras, Projective Quadrics, and Spin Groups, Conformal Groups in Geometry and Spin Structures, Volume 50 (2008), p. 1 | DOI:10.1007/978-0-8176-4643-1_1
- Pseudounitary Conformal Spin Structures, Conformal Groups in Geometry and Spin Structures, Volume 50 (2008), p. 205 | DOI:10.1007/978-0-8176-4643-1_3
- Real Conformal Spin Structures, Conformal Groups in Geometry and Spin Structures, Volume 50 (2008), p. 71 | DOI:10.1007/978-0-8176-4643-1_2
- (Co)bordism groups in quantum super PDE's. III: Quantum super Yang–Mills equations, Nonlinear Analysis: Real World Applications, Volume 8 (2007) no. 2, p. 447 | DOI:10.1016/j.nonrwa.2005.12.006
- Partially massless spin-2 electrodynamics, Physical Review D, Volume 74 (2006) no. 8 | DOI:10.1103/physrevd.74.084036
- Constant curvature algebras and higher spin action generating functions, Nuclear Physics B, Volume 724 (2005) no. 3, p. 453 | DOI:10.1016/j.nuclphysb.2005.06.021
- Mode solutions of the Klein-Gordon equation in warped spacetimes †, Classical and Quantum Gravity, Volume 18 (2001) no. 2, p. 207 | DOI:10.1088/0264-9381/18/2/301
- Partial masslessness of higher spins in (A)dS, Nuclear Physics B, Volume 607 (2001) no. 3, p. 577 | DOI:10.1016/s0550-3213(01)00212-7
- (Dis)continuities of massless limits in spin-3/2-mediated interactions and cosmological supergravity, Physics Letters B, Volume 501 (2001) no. 1-2, p. 134 | DOI:10.1016/s0370-2693(01)00109-5
- REVIEW OF FUNDAMENTAL NOTIONS OF ANALYSIS, Analysis, Manifolds and Physics (2000), p. 1 | DOI:10.1016/b978-044450473-9/50003-8
- On the Duffin-Kemmer-Petiau formulation of the covariant Hamiltonian dynamics in field theory, Reports on Mathematical Physics, Volume 46 (2000) no. 1-2, p. 107 | DOI:10.1016/s0034-4877(01)80013-6
- The evolution of the Dirac field in curved space-times, manuscripta mathematica, Volume 88 (1995) no. 1, p. 233 | DOI:10.1007/bf02567820
- On the concepts of Lie and covariant derivatives of spinors. I, Journal of Physics A: Mathematical and General, Volume 27 (1994) no. 13, p. 4569 | DOI:10.1088/0305-4470/27/13/030
- On the concepts of Lie and covariant derivatives of spinors: part II, Journal of Physics A: Mathematical and General, Volume 27 (1994) no. 17, p. 5941 | DOI:10.1088/0305-4470/27/17/026
- S, Encyclopaedia of Mathematics (1992), p. 197 | DOI:10.1007/978-94-015-1235-0_2
- Quantum geometry of PDE's, Reports on Mathematical Physics, Volume 30 (1991) no. 3, p. 273 | DOI:10.1016/0034-4877(91)90063-s
- Quantization of reimannian gravity: Heisenberg representation, Foundations of Physics Letters, Volume 3 (1990) no. 2, p. 179 | DOI:10.1007/bf00689884
- Cauchy's problem and Huygens' principle for the linearized Einstein field equations, General Relativity and Gravitation, Volume 22 (1990) no. 8, p. 843 | DOI:10.1007/bf00763226
- Covariant, algebraic, and operator spinors, International Journal of Theoretical Physics, Volume 29 (1990) no. 4, p. 371 | DOI:10.1007/bf00674438
- Bibliography, Orthogonal and Symplectic Clifford Algebras (1990), p. 332 | DOI:10.1007/978-94-015-7877-6_23
- Non-factorizable separable systems and higher-order symmetries of the Dirac operator, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, Volume 428 (1990) no. 1874, p. 229 | DOI:10.1098/rspa.1990.0032
- Fourier Transform in Non-Euclidean Space and its Applications to Physics, Recent Advances in Fourier Analysis and Its Applications (1990), p. 41 | DOI:10.1007/978-94-009-0665-5_4
- Parallel spinors and parallel forms, Annals of Global Analysis and Geometry, Volume 7 (1989) no. 1, p. 59 | DOI:10.1007/bf00137402
- On the perturbation problem associated to isometric embeddings of Riemannian manifolds, Annals of Global Analysis and Geometry, Volume 7 (1989) no. 1, p. 69 | DOI:10.1007/bf00137403
- BIBLIOGRAPHY, Huygens' Principle and Hyperbolic Equations (1988), p. 833 | DOI:10.1016/b978-0-12-307330-3.50024-6
- The natural spinor connection on S 8 is a gauge field, Letters in Mathematical Physics, Volume 11 (1986) no. 2, p. 171 | DOI:10.1007/bf00398429
- On the zero-mode structure of the Rarita-Schwinger operator, Classical and Quantum Gravity, Volume 2 (1985) no. 5, p. L109 | DOI:10.1088/0264-9381/2/5/003
- Cauchy's problem and Huygens' principle for relativistic higher spin wave equations in an arbitrary curved space-time, General Relativity and Gravitation, Volume 17 (1985) no. 1, p. 15 | DOI:10.1007/bf00760104
- Weak and strong quantum vacua in Bianchi type-I universes, Physical Review D, Volume 31 (1985) no. 4, p. 742 | DOI:10.1103/physrevd.31.742
- On the elimination of Pauli couplings in Kaluza-Klein theories using torsion, Physics Letters B, Volume 159 (1985) no. 4-6, p. 279 | DOI:10.1016/0370-2693(85)90250-3
- Intertwining differential operators for spinor-form representations of the conformal group, Advances in Mathematics, Volume 54 (1984) no. 1, p. 1 | DOI:10.1016/0001-8708(84)90034-3
- Clifford analysis of exterior forms and Fermi-Bose symmetry, Journal of Physics A: Mathematical and General, Volume 16 (1983) no. 17, p. 4147 | DOI:10.1088/0305-4470/16/17/029
- Conformally covariant nonlinear equations on tensor-spinors, Letters in Mathematical Physics, Volume 7 (1983) no. 1, p. 63 | DOI:10.1007/bf00398714
- A relation between local and total energy in general relativity, Communications in Mathematical Physics, Volume 85 (1982) no. 3, p. 429 | DOI:10.1007/bf01208723
- The general relativistic hydrogen atom, Communications in Mathematical Physics, Volume 86 (1982) no. 1, p. 69 | DOI:10.1007/bf01205662
- Quantum field theory on curved space-time: an axiomatic approach, Il Nuovo Cimento A, Volume 67 (1982) no. 4, p. 305 | DOI:10.1007/bf02902594
- Gravitational Energy Cannot Become Negative, Physical Review Letters, Volume 48 (1982) no. 6, p. 371 | DOI:10.1103/physrevlett.48.371
- Solution globale des equations de Maxwell-Dirac-Klein-Gordon, Rendiconti del Circolo Matematico di Palermo, Volume 31 (1982) no. 2, p. 267 | DOI:10.1007/bf02844359
- Quantum field theory in curved space-time. Massive and massless vector fields, Physical Review D, Volume 24 (1981) no. 10, p. 2576 | DOI:10.1103/physrevd.24.2576
- Geometric methods in classical field theory, Physics Reports, Volume 75 (1981) no. 3, p. 125 | DOI:10.1016/0370-1573(81)90155-1
- The quantum equivalence principle and the particle model in curved space-time, Il Nuovo Cimento A, Volume 60 (1980) no. 2, p. 138 | DOI:10.1007/bf02902442
- Selbstadjungierte huygenssche Differentialgleichungen zweiter Ordnung für nichtskalare Spintensorfelder, Mathematische Nachrichten, Volume 94 (1980) no. 1, p. 211 | DOI:10.1002/mana.19800940114
- New exact solution to the Einstein-Dirac equations, Physical Review D, Volume 19 (1979) no. 6, p. 1635 | DOI:10.1103/physrevd.19.1635
- The problem of scalar field theory in curved space-time, General Relativity and Gravitation, Volume 9 (1978) no. 2, p. 101 | DOI:10.1007/bf00760147
- Some Remarks on the Fundamental Kernels of a Pseudo-Riemannian Manifold, Differential Geometry and Relativity (1976), p. 55 | DOI:10.1007/978-94-010-1508-0_7
- Quantum gravidynamics. II. Path integrals with spin, Journal of Physics A: Mathematical and General, Volume 8 (1975) no. 1, p. 29 | DOI:10.1088/0305-4470/8/1/008
- Fibrations spinorielles et twisteurs généralisés, Periodica Mathematica Hungarica, Volume 6 (1975) no. 2, p. 143 | DOI:10.1007/bf02018816
- The characteristic surfaces of a classical spin-3/2 field in an Einstein-Maxwell background, Physics Letters B, Volume 55 (1975) no. 2, p. 217 | DOI:10.1016/0370-2693(75)90446-3
- A new approach to interacting fields, International Journal of Theoretical Physics, Volume 10 (1974) no. 6, p. 391 | DOI:10.1007/bf01807640
- Considérations sur les structures spinorielles, Rendiconti del Circolo Matematico di Palermo, Volume 23 (1974) no. 2-3, p. 113 | DOI:10.1007/bf02843660
- On the neutrino in general relativity, Lettere al Nuovo Cimento, Volume 5 (1972) no. 1, p. 48 | DOI:10.1007/bf02832770
- Dérivées de Lie des spineurs, Annali di Matematica Pura ed Applicata, Volume 91 (1971) no. 1, p. 317 | DOI:10.1007/bf02428822
- On the geometric structure of a parity-conserving relativistic quantum field theory, International Journal of Theoretical Physics, Volume 4 (1971) no. 4, p. 305 | DOI:10.1007/bf00674284
- Remarks on unified field structures, spin structures and canonical quantization, International Journal of Theoretical Physics, Volume 3 (1970) no. 4, p. 289 | DOI:10.1007/bf00669756
- Some theorems on spinor-tensors, Annali di Matematica Pura ed Applicata, Volume 76 (1967) no. 1, p. 1 | DOI:10.1007/bf02412225
- Equilibrium of a Large Assembly of Particles in General Relativity, Physical Review, Volume 148 (1966) no. 4, p. 1269 | DOI:10.1103/physrev.148.1269
Cité par 75 documents. Sources : Crossref