The DOI matches its Crossref record.
Spinors and Space-Time
Abstract
This volume introduces and systematically develops the calculus of 2-spinors. This is the first detailed exposition of this technique which leads not only to a deeper understanding of the structure of space-time, but also provides shortcuts to some very tedious calculations. Many results are given here for the first time.
Overview
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“For those who are accustomed to using the spinorial description of relativistic particles, the photon wave function is a familiar object. It is the self-dual (or anti self-dual) part of the electromagnetic field tensor (cf. Ref. [29]).”
From On the Wave Function of the Photon (1994) · cites this paper as [29]
In the citing paper
“In. the spinorial formalism, our observation that in curved space both helicities propagate without mixing is a simple consequence of the fact that both spinors φAB and φA'B' satisfy separate equations of the form [29]”
From On the Wave Function of the Photon (1994) · cites this paper as [29]
In the citing paper
“3. classical Dirac fields [necessarily] (Penrose and Rindler 1984)”
From A Primer on Energy Conditions (2017) · cites this paper as Penrose and Rindler 1984
Citations
Cited by
Sorted by citations
Items 401–500 of 1,000
Null vectors, spinors, and strings
Budinich, P. (1986) · Communications in Mathematical Physics · doi:10.1007/bf01220999 · Cited by 30
Stochastic dynamics of the scattering amplitude generating K-distributed noise
Field, T. R., & Tough, R. J. A. (2003) · Journal of Mathematical Physics · doi:10.1063/1.1611264 · Cited by 30
Relativistic dynamics of charges in electromagnetic fields: An eigenspinor approach
Baylis, W. E., & Yao, Y. (1999) · Physical Review A · doi:10.1103/physreva.60.785 · Cited by 30
Holomorphic Linking, Loop Equations and Scattering Amplitudes in Twistor SpacePreprint
Bullimore, M. R., & Skinner, D. B. (2011) · arXiv (Cornell University) · doi:10.48550/arxiv.1101.1329 · Cited by 30
Spinors in Higher Dimensional and Locally Anisotropic SpacesPreprint
Vacaru, S. I. (1996) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/9604015 · Cited by 30
The Big Bang and its Dark-Matter Content: Whence, Whither, and Wherefore
Penrose, R. (2018) · Foundations of Physics · doi:10.1007/s10701-018-0162-3 · Cited by 26
Self-citationSpinning geometry = Twisted geometry
Freidel, L., & Ziprick, J. (2014) · Classical and Quantum Gravity · doi:10.1088/0264-9381/31/4/045007 · Cited by 43
Teleportation of quantum resources and quantum Fisher information under Unruh effect
Jafarzadeh, M., Jahromi, H. R., & Amniat-Talab, M. (2018) · Quantum Information Processing · doi:10.1007/s11128-018-1922-x · Cited by 29
Polyhomogeneous Expansions Close to Null and Spatial Infinity
Kroon, J. A. V. (2002) · Lecture notes in physics · doi:10.1007/3-540-45818-2_7 · Cited by 29
Shear free solutions in general relativity theory
Ellis, G. F. R. (2011) · General Relativity and Gravitation · doi:10.1007/s10714-011-1244-0 · Cited by 29
Conformally Covariant Systems of Wave Equations and their Equivalence to Einstein’s Field Equations
Paetz, T.-T. (2014) · Annales Henri Poincaré · doi:10.1007/s00023-014-0359-8 · Cited by 29
The twistor spinors of generic 2- and 3-distributions
Hammerl, M., & Sagerschnig, K. (2010) · Annals of Global Analysis and Geometry · doi:10.1007/s10455-010-9240-2 · Cited by 29
Curvature of Hessian manifolds
Амари, Ш.-И., & Armstrong, J. (2014) · Differential Geometry and its Applications · doi:10.1016/j.difgeo.2014.01.001 · Cited by 29
4D higher spin black holes with nonlinear scalar fluctuations
Iazeolla, C., & Sundell, P. (2017) · Journal of High Energy Physics · doi:10.1007/jhep10(2017)130 · Cited by 29
Cosmological Einstein-Maxwell instantons and Euclidean supersymmetry: anti-self-dual solutions
Dunajski, M., Gutowski, J., Sabra, W., et al. (2011) · Research Portal (King's College London) · Cited by 29
Symmetry operators for Maxwell’s equations on curved space-time
Kalnins, E. G., McLenaghan, R. G., & Williams, G. (1992) · Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences · doi:10.1098/rspa.1992.0136 · Cited by 29
Dynamics of Cosmic Strings and Other Brane Models
Carter, B. (1995) · NATO ASI series. Series B : Physics · doi:10.1007/978-1-4615-1883-9_12 · Cited by 29
The Teukolsky–Starobinsky identities in type D vacuum backgrounds with cosmological constant
del Castillo, G. F. T. (1988) · Journal of Mathematical Physics · doi:10.1063/1.527865 · Cited by 29
Spinor-helicity formalism for massless fields in AdS4. Part II. Potentials
Nagaraj, B., & Ponomarev, D. (2020) · Journal of High Energy Physics · doi:10.1007/jhep06(2020)068 · Cited by 28
Comparing remnant properties from horizon data and asymptotic data in numerical relativity
Iozzo, D. A. B., Khera, N., Stein, L. C., et al. (2021) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.103.124029 · Cited by 28
The generalized Heun equation in QFT in curved spacetimes
Batic, D., Schmid, H., & Winklmeier, M. (2006) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/39/40/019 · Cited by 28
Angular momentum of isolated systems
Helfer, A. D. (2007) · General Relativity and Gravitation · doi:10.1007/s10714-007-0509-0 · Cited by 28
Self-dual supergravity and twistor theory
Wolf, M. (2007) · Classical and Quantum Gravity · doi:10.1088/0264-9381/24/24/010 · Cited by 28
Killing–Yano tensors and variable separation in Kerr geometry
Kalnins, E. G., Miller, W., & Williams, G. (1989) · Journal of Mathematical Physics · doi:10.1063/1.528565 · Cited by 28
On energy-critical half-wave maps into $${\mathbb {S}}^2$$ S 2
Lenzmann, E., & Schikorra, A. (2018) · Inventiones mathematicae · doi:10.1007/s00222-018-0785-1 · Cited by 28
Finkelstein, D. (1986) · Physical Review Letters · doi:10.1103/physrevlett.56.1532 · Cited by 28
The Dirac Propagator in the Kerr-Newman Metric
Batic, D., & Schmid, H. (2006) · Progress of Theoretical Physics · doi:10.1143/ptp.116.517 · Cited by 28
Maxwell Equations—The One-Photon Quantum Equation
Gersten, A. (2001) · Foundations of Physics · doi:10.1023/a:1017551920941 · Cited by 30
The Dirac equation in the Robertson–Walker space–time
Zecca, A. (1996) · Journal of Mathematical Physics · doi:10.1063/1.531436 · Cited by 28
Dirac fields on asymptotically flat space-times
Nicolas, J.-P. (2002) · Dissertationes Mathematicae · doi:10.4064/dm408-0-1 · Cited by 28
The geometry of coherent states
Field, T. R., & Hughston, L. P. (1999) · Journal of Mathematical Physics · doi:10.1063/1.532716 · Cited by 28
Relativistic Physics in Arbitrary Reference FramesPreprint
Mit︠s︡kevich, N. V. (2005) · arXiv (Cornell University) · Cited by 28
El‐Nabulsi, R. A. (2009) · International Journal of Geometric Methods in Modern Physics · doi:10.1142/s021988780900345x · Cited by 27
Some remarks on (super)-conformal Killing-Yano tensors
Howe, P., & Lindström, U. (2018) · Journal of High Energy Physics · doi:10.1007/jhep11(2018)049 · Cited by 27
Emergence of classical behavior in the early Universe
Ashtekar, A., Corichi, A., & Kesavan, A. (2020) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.102.023512 · Cited by 31
Cisterna, A., Díaz, F., Mann, R. B., & Oliva, J. (2023) · Journal of High Energy Physics · doi:10.1007/jhep11(2023)073 · Cited by 27
100 Years of General Relativity
Ellis, G. (2015) · Cambridge University Press eBooks · doi:10.1017/cbo9781139583961.003 · Cited by 33
Correlation functions, null polygonal Wilson loops, and local operators
Adamo, T. (2011) · Journal of High Energy Physics · doi:10.1007/jhep12(2011)006 · Cited by 27
Conformal Yano–Killing tensors for the Taub–NUT metric
Jezierski, J., & Łukasik, M. (2007) · Classical and Quantum Gravity · doi:10.1088/0264-9381/24/5/015 · Cited by 27
Finkelstein, D., Finkelstein, S. R., & Holm, C. (1986) · International Journal of Theoretical Physics · doi:10.1007/bf00670769 · Cited by 27
An ansatz for almost-Kähler, Einstein 4-manifolds
Armstrong, J. (2002) · Journal für die reine und angewandte Mathematik (Crelles Journal) · doi:10.1515/crll.2002.009 · Cited by 27
THE LIE DERIVATIVE OF SPINOR FIELDS: THEORY AND APPLICATIONS
GODINA, M., & MATTEUCCI, P. (2005) · International Journal of Geometric Methods in Modern Physics · doi:10.1142/s0219887805000624 · Cited by 27
Harnett, G. (1991) · Journal of Mathematical Physics · doi:10.1063/1.529098 · Cited by 27
Reductive G-structures and Lie derivativesPreprint
Godina, M., & Matteucci, P. (2002) · Cited by 27
10 Understanding Quaternions and the Dirac Belt TrickPreprint
Staley, M. (2010) · Cited by 27
Infinity in string cosmology: A review through open problems
Antoniadis, I., & Cotsakis, S. (2016) · International Journal of Modern Physics D · doi:10.1142/s0218271817300099 · Cited by 7
Asymptotic structure with a positive cosmological constant
Fernández-Álvarez, F., & Senovilla, J. M. M. (2021) · Classical and Quantum Gravity · doi:10.1088/1361-6382/ac395b · Cited by 26
Decay of solutions to the Maxwell equation on the Schwarzschild background
Andersson, L., Bäckdahl, T., & Blue, P. (2016) · Classical and Quantum Gravity · doi:10.1088/0264-9381/33/8/085010 · Cited by 26
Gravity with a cosmological constant from rational curves
Adamo, T. (2015) · Journal of High Energy Physics · doi:10.1007/jhep11(2015)098 · Cited by 25
Gravitational anomaly and Hawking radiation near a weakly isolated horizon
Wu, X., Huang, C.-G., & Sun, J.-R. (2008) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.77.124023 · Cited by 28
The relation between metric and spin-2 formulations of linearized Einstein theory
Jezierski, J. (1995) · General Relativity and Gravitation · doi:10.1007/bf02113066 · Cited by 26
On the density of twistor elementary states
Eastwood, M., & Pilato, A. M. (1991) · Pacific Journal of Mathematics · doi:10.2140/pjm.1991.151.201 · Cited by 26
Han, D., Kim, Y. S., & Noz, M. E. (1989) · Physical Review A · doi:10.1103/physreva.40.902 · Cited by 24
Lump Dynamics in the ℂ P 1 Model on the Torus
Speight, M. (1998) · Communications in Mathematical Physics · doi:10.1007/s002200050367 · Cited by 26
Why odd-space and odd-time dimensions in even-dimensional spaces?
Borštnik, N. M., & NIELSEN, H. B. (2000) · Physics Letters B · doi:10.1016/s0370-2693(00)00775-9 · Cited by 30
A nonlinear Klein–Gordon equation on Kerr metrics
Nicolas, J.-P. (2002) · Journal de Mathématiques Pures et Appliquées · doi:10.1016/s0021-7824(02)01272-2 · Cited by 26
Nambu-type generalization of the Dirac equation
Czachor, M. (1997) · Physics Letters A · doi:10.1016/s0375-9601(96)00869-9 · Cited by 26
FromD-bar D Pairs to Branes in Motion
Myers, R. C., & Winters, D. (2002) · Journal of High Energy Physics · doi:10.1088/1126-6708/2002/12/061 · Cited by 26
Einstein's equations and the embedding of 3-dimensional CR manifolds
Hill, C. D., Lewandowski, J., & Nurowski, P. (2008) · Indiana University Mathematics Journal · doi:10.1512/iumj.2008.57.3473 · Cited by 25
Anti–de Sitter Particles and Manifest (Super)Isometries
Arvanitakis, A. S., Barns-Graham, A. E., & Townsend, P. K. (2017) · Physical Review Letters · doi:10.1103/physrevlett.118.141601 · Cited by 25
Spinor-helicity and the algebraic classification of higher-dimensional spacetimes
Monteiro, R., Nicholson, I., & O’Connell, D. (2019) · Classical and Quantum Gravity · doi:10.1088/1361-6382/ab03df · Cited by 25
Majorana representation for mixed states
Serrano-Ensástiga, E., & Braun, D. (2020) · Physical Review A · doi:10.1103/physreva.101.022332 · Cited by 25
Sati, H., & Schreiber, U. (2022) · Advances in Theoretical and Mathematical Physics · doi:10.4310/atmp.2022.v26.n4.a4 · Cited by 25
Gluon Scattering on Self-Dual Radiative Gauge Fields
Adamo, T., MASON, L. J., & Sharma, A. (2022) · Communications in Mathematical Physics · doi:10.1007/s00220-022-04582-9 · Cited by 37
Locally Anisotropic Structures and Nonlinear Connections in Einstein and Gauge Gravity
Vacaru, S. I., & Dehnen, H. (2003) · General Relativity and Gravitation · doi:10.1023/a:1022388909622 · Cited by 25
Equivalence of three-dimensional spacetimes
Sousa, F. C., Fonseca–Neto, J. B., & Romero, C. (2008) · Classical and Quantum Gravity · doi:10.1088/0264-9381/25/3/035007 · Cited by 25
The ?-field theory of gravitation and cosmology
Yu, X. F. (1989) · Astrophysics and Space Science · doi:10.1007/bf00642814 · Cited by 25
LIGHT-CONE GAUGE HAMILTONIAN FOR AdS4 × ℂℙ3 SUPERSTRING
Uvarov, D. V. (2010) · Modern Physics Letters A · doi:10.1142/s0217732310033153 · Cited by 25
Classical and quantum aspects of electric-magnetic duality rotations in curved spacetimes
Agulló, I., del Río, A., & Navarro-Salas, J. (2018) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.98.125001 · Cited by 26
Recent advances in the use of separation of variables methods in general relativity
Kalnins, E. G., Miller, W., & Williams, G. (1992) · Philosophical Transactions of the Royal Society of London Series A Physical and Engineering Sciences · doi:10.1098/rsta.1992.0071 · Cited by 25
MAXWELL FIELD ON THE POINCARÉ GROUP
Варламов, В. В. (2005) · International Journal of Modern Physics A · doi:10.1142/s0217751x05025048 · Cited by 25
Classical aspects of lightlike dimensional reduction
Minguzzi, E. (2006) · Classical and Quantum Gravity · doi:10.1088/0264-9381/23/23/029 · Cited by 25
Note on (conformally) semi-symmetric spacetimes
Eriksson, I., & Senovilla, J. M. M. (2009) · Classical and Quantum Gravity · doi:10.1088/0264-9381/27/2/027001 · Cited by 25
Complex visibilities of cosmic microwave background anisotropies
Ng, K. (2001) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.63.123001 · Cited by 25
Twistor spaces and harmonic maps
Davidov, J., & Сергеев, А. Г. (1993) · Russian Mathematical Surveys · doi:10.1070/rm1993v048n03abeh001031 · Cited by 25
2-Spinors, Twistors and Supersymmetry in the Spacetime Algebras
Lasenby, A. N., Doran, C., & Gull, S. (1993) · Springer eBooks · doi:10.1007/978-94-011-1719-7_28 · Cited by 25
On Supertwistors, the Penrose-Ward Transform and N=4 super Yang-Mills TheoryPreprint
Popov, A. D., & Saemann, C. (2004) · arXiv (Cornell University) · doi:10.48550/arxiv.hep-th/0405123 · Cited by 25
François, J. (2021) · Journal of High Energy Physics · doi:10.1007/jhep03(2021)225 · Cited by 24
On cosmological mass with positive Λ
Penrose, R. (2011) · General Relativity and Gravitation · doi:10.1007/s10714-011-1255-x · Cited by 24
Self-citationType III and N Einstein spacetimes in higher dimensions: General properties
Ortaggio, M., Pravda, V., & Pravdová, A. (2010) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.82.064043 · Cited by 24
Asymptotic directional structure of radiative fields in spacetimes with a cosmological constant
Krtouš, P., & Podolský, J. (2004) · Classical and Quantum Gravity · doi:10.1088/0264-9381/21/24/r01 · Cited by 24
Regularity at space-like and null infinity
MASON, L. J., & Nicolas, J.-P. (2008) · Journal of the Institute of Mathematics of Jussieu · doi:10.1017/s1474748008000297 · Cited by 24
Topological two-form gravity in four dimensions
Lee, H. Y., Nakamichi, A., & Ueno, T. (1993) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.47.1563 · Cited by 23
Classification of Kerr–de Sitter-like spacetimes with conformally flat I *
Mars, M., Paetz, T.-T., & Senovilla, J. M. M. (2017) · Classical and Quantum Gravity · doi:10.1088/1361-6382/aa5dc2 · Cited by 24
Garat, A. (2017) · International Journal of Geometric Methods in Modern Physics · doi:10.1142/s0219887817501328 · Cited by 24
Numerical Methods for the Einstein Equations in Null Quasi-Spherical Coordinates
Bartnik, R., & Norton, A. H. (2000) · SIAM Journal on Scientific Computing · doi:10.1137/s1064827599356171 · Cited by 24
Maxwell Fields and Shear-Free Null Geodesic Congruences
Newman, E. (2004) · CERN Document Server (European Organization for Nuclear Research) · Cited by 24
The Wave Equation on Singular Space-Times
Grant, J. D. E., Mayerhofer, E., & Steinbauer, R. (2008) · Surrey Research Insight Open Access (The University of Surrey) · Cited by 24
The separability of Maxwell’s equations in type-D backgrounds
del Castillo, G. F. T. (1988) · Journal of Mathematical Physics · doi:10.1063/1.527993 · Cited by 24
Complete null data for a black hole collision
Gómez, R., Husa, S., & Winicour, J. (2001) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.64.024010 · Cited by 24
Einstein's Equation in Ashtekar's Variables Constitutes a Symmetric Hyperbolic System
Iriondo, M. S., Leguizamón, E. O., & Reula, O. A. (1997) · Physical Review Letters · doi:10.1103/physrevlett.79.4732 · Cited by 24
Wave-particle dualism and the interpretation of quantum mechanics
Dewdney, C., Horton, G., Lam, M. M., et al. (1992) · Foundations of Physics · doi:10.1007/bf01889712 · Cited by 24
Sasakian Geometry, Holonomy, and SupersymmetryPreprint
Boyer, C. P., & Galicki, K. (2007) · arXiv (Cornell University) · doi:10.48550/arxiv.math/0703231 · Cited by 24
1 Shear free solutions in General Relativity TheoryPreprint
Ellis, G. (2013) · Cited by 24
The Kummer tensor density in electrodynamics and in gravity
Baekler, P., Favaro, A., Itin, Y., et al. (2014) · Kölner Universitäts PublikationsServer (Universität zu Köln) · Cited by 23
Garat, A. (2020) · Reports on Mathematical Physics · doi:10.1016/s0034-4877(20)30088-4 · Cited by 23
Ma, S., Wang, Q., Deppe, N., Hébert, F., Kidder, L., Moxon, J., Throwe, W., Vu, N. L., Scheel, M., & Chen, Y. (2022) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.105.104007 · Cited by 23
New Hamiltonian formalism and quasilocal conservation equations of general relativity
Yoon, J. H. (2004) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.70.084037 · Cited by 23
Unique characterization of the Bel–Robinson tensor
Bergqvist, G., & Lankinen, P. (2004) · Classical and Quantum Gravity · doi:10.1088/0264-9381/21/14/012 · Cited by 23
Massive twistor particle with spin generated by Souriau–Wess–Zumino term and its quantization
Fedoruk, S., & Lukierski, J. (2014) · Physics Letters B · doi:10.1016/j.physletb.2014.04.059 · Cited by 23
Metadata
- Authors
- Penrose, R., & Rindler, W.
- Venue
- Cambridge University Press eBooks
- Publisher
- Cambridge University Press
- Published
- 1984-10-18
- OpenAlex
- W1789645782
- Cited by
- 2,172
- References
- 0
- Citations by year
- 2026: 42 · 2025: 47 · 2024: 36 · 2023: 62 · 2022: 66 · 2021: 82 · 2020: 50 · 2019: 54 · 2018: 55 · 2017: 53 · 2016: 63 · 2015: 55 · 2014: 69 · 2013: 76 · 2012: 60
- FWCI
- 14.09
- Type
- book
- Language
- en
- Open access
- closed
- Locations
- Cambridge University Press eBooks (publishedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Mathematics › Applied Mathematics › Algebraic and Geometric Analysis
- Physical Sciences › Mathematics › Geometry and Topology › Advanced Differential Geometry Research
- Keywords
- spinor calculus, spacetime structure, general relativity, differential geometry
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
