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 101–200 of 1,000
A Complete Set of Riemann Invariants
Zakhary, E., & McIntosh, C. B. G. (1997) · General Relativity and Gravitation · doi:10.1023/a:1018851201784 · Cited by 90
The Einstein-Elko system – Can dark matter drive inflation?
Böhmer, C. G. (2007) · Annalen der Physik · doi:10.1002/andp.200610237 · Cited by 100
Generalization of the Geroch–Held–Penrose formalism to higher dimensions
Durkee, M., Pravda, V., Pravdová, A., & Reall, H. S. (2010) · Classical and Quantum Gravity · doi:10.1088/0264-9381/27/21/215010 · Cited by 89
A gravitational entropy proposal
Clifton, T., Ellis, G. F. R., & Tavakol, R. (2013) · Classical and Quantum Gravity · doi:10.1088/0264-9381/30/12/125009 · Cited by 88
Exotic statistics for strings in 4d BF theory
Baez, J. C., Crans, A. S., & Wise, D. K. (2007) · Advances in Theoretical and Mathematical Physics · doi:10.4310/atmp.2007.v11.n5.a1 · Cited by 92
Classification of local generalized symmetries for the vacuum Einstein equations
Anderson, I. M., & Torre, C. G. (1996) · Communications in Mathematical Physics · doi:10.1007/bf02099248 · Cited by 87
The classification of subfactors of index at most 5
Jones, V. F. R., Morrison, S., & Snyder, N. (2013) · Bulletin of the American Mathematical Society · doi:10.1090/s0273-0979-2013-01442-3 · Cited by 104
States and operators in the spacetime algebra
Doran, C., Lasenby, A. N., & Gull, S. F. (1993) · Foundations of Physics · doi:10.1007/bf01883678 · Cited by 86
Каллош, Р. (1992) · Physics Letters B · doi:10.1016/0370-2693(92)90482-j · Cited by 86
GA-SIFT: A new scale invariant feature transform for multispectral image using geometric algebra
Li, Y., Liu, W., Xiao-tang, L., Huang, Q., & Li, X. (2014) · Information Sciences · doi:10.1016/j.ins.2013.12.022 · Cited by 83
The BMS4 algebra at spatial infinity
Troessaert, C. (2018) · Classical and Quantum Gravity · doi:10.1088/1361-6382/aaae22 · Cited by 85
1 Vanishing Scalar Invariant Spacetimes in Higher DimensionsPreprint
Coley, A., Milson, R., Pravda, V., et al. (2004) · Cited by 85
Positivity of quasi-local mass II
Liu, C.-C. M., & Yau, S. (2005) · Journal of the American Mathematical Society · doi:10.1090/s0894-0347-05-00497-2 · Cited by 77
Scattering amplitudes and Wilson loops in twistor space
Adamo, T., Bullimore, M. R., MASON, L. J., et al. (2011) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/44/45/454008 · Cited by 84
Asymptotics with a positive cosmological constant. III. The quadrupole formula
Ashtekar, A., Bonga, B., & Kesavan, A. (2015) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.92.104032 · Cited by 83
Scattering Amplitudes and BCFW Recursion in Twistor SpacePreprint
MASON, L. J., & Skinner, D. B. (2009) · Cited by 83
Energy of isolated systems at retarded times as the null limit of quasilocal energy
Brown, J. D., Lau, S. R., & York, J. W. (1997) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.55.1977 · Cited by 73
Elementary formula for entanglement entropies of fermionic systems
Lévay, P., Nagy, S., & Pipek, J. (2005) · Physical Review A · doi:10.1103/physreva.72.022302 · Cited by 79
Owen, R., Brink, J., Chen, Y., et al. (2011) · Physical Review Letters · doi:10.1103/physrevlett.106.151101 · Cited by 79
Statistical geometry in quantum mechanics
Brody, D. C., & Hughston, L. P. (1998) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.1998.0266 · Cited by 89
Anti-self-dual Yang–Mills equations on noncommutative space–time
Takasaki, K. (2001) · Journal of Geometry and Physics · doi:10.1016/s0393-0440(00)00056-5 · Cited by 78
REVIEW: The Rest-Frame Instant Form of Metric Gravity
Lusanna, L. (2001) · General Relativity and Gravitation · doi:10.1023/a:1012297028267 · Cited by 81
Weyl Double Copy for Gravitational Waves
Godazgar, H., Godazgar, M., Monteiro, R., et al. (2021) · Physical Review Letters · doi:10.1103/physrevlett.126.101103 · Cited by 78
Black hole thermodynamics in the presence of nonlinear electromagnetic fields
Bokulić, A., Smolić, I., & Jurić, T. (2021) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.103.124059 · Cited by 86
Neitzke, A., Pioline, B., & Vandoren, S. (2007) · Journal of High Energy Physics · doi:10.1088/1126-6708/2007/04/038 · Cited by 78
Nichols, D. A., Owen, R., Zhang, F., et al. (2011) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.84.124014 · Cited by 78
Stringy black holes and the geometry of entanglement
Lévay, P. (2006) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.74.024030 · Cited by 76
Striking property of the gravitational Hamiltonian
Ashtekar, A., & Varadarajan, M. (1994) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.50.4944 · Cited by 77
Newman, E. T. (2002) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.65.104005 · Cited by 78
Actions for self-dual Higher Spin Gravities
Krasnov, K. V., Skvortsov, E. D., & Tran, T. (2021) · Journal of High Energy Physics · doi:10.1007/jhep08(2021)076 · Cited by 77
Rotating black holes at future colliders. III. Determination of black hole evolution
Ida, D., Oda, K.-Y., & Park, S. C. (2006) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.73.124022 · Cited by 90
The BMS4 algebra at spatial infinity
Troessaert, C. (2018) · MPG.PuRe (Max Planck Society) · Cited by 75
Generalized pseudo-Riemannian geometry
Kunzinger, M., & Steinbauer, R. (2002) · Transactions of the American Mathematical Society · doi:10.1090/s0002-9947-02-03058-1 · Cited by 75
Invariant Theory and Calculus for Conformal Geometries
Gover, A. R. (2001) · Advances in Mathematics · doi:10.1006/aima.2001.1999 · Cited by 75
A proof of the correlation function/supersymmetric Wilson loop correspondence
Adamo, T., Bullimore, M. R., MASON, L. J., et al. (2011) · Journal of High Energy Physics · doi:10.1007/jhep08(2011)076 · Cited by 74
Hawking radiation in large N strongly coupled field theories
Hubeny, V. E., Marolf, D., & Rangamani, M. (2010) · Classical and Quantum Gravity · doi:10.1088/0264-9381/27/9/095015 · Cited by 52
Metric Connections in Projective Differential Geometry
Eastwood, M., & Matveev, V. S. (2008) · The IMA volumes in mathematics and its applications · doi:10.1007/978-0-387-73831-4_16 · Cited by 74
On static and radiative space-times
Friedrich, H. (1988) · Communications in Mathematical Physics · doi:10.1007/bf01218260 · Cited by 74
Black hole boundary conditions and coordinate conditions
Eardley, D. M. (1998) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.57.2299 · Cited by 74
Jordan, A. N., & Korotkov, A. N. (2006) · Physical Review B · doi:10.1103/physrevb.74.085307 · Cited by 73
Is Newtonian Cosmology Really Inconsistent?
Malament, D. B. (1995) · Philosophy of Science · doi:10.1086/289882 · Cited by 71
Prolongations of geometric overdetermined systems
Branson, T., Čap, A., Eastwood, M., et al. (2004) · Cited by 72
Universal Teukolsky equations and black hole perturbations in higher-derivative gravity
Cano, P. A., Fransen, K., Hertog, T., et al. (2023) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.108.024040 · Cited by 72
Scattering amplitudes and BCFW recursion in twistor space
Mason, L., & Skinner, D. (2010) · Journal of High Energy Physics · doi:10.1007/jhep01(2010)064 · Cited by 72
Relativistic Bennett-Brassard cryptographic scheme, relativistic errors, and how to correct them
Czachor, M., & Wilczewski, M. (2003) · Physical Review A · doi:10.1103/physreva.68.010302 · Cited by 72
Twistor-strings, Grassmannians and leading singularities
Bullimore, M. R., MASON, L. J., & Skinner, D. B. (2010) · Journal of High Energy Physics · doi:10.1007/jhep03(2010)070 · Cited by 72
Dual-null dynamics of the Einstein field
Hayward, S. A. (1993) · Classical and Quantum Gravity · doi:10.1088/0264-9381/10/4/013 · Cited by 72
New boundary variables for classical and quantum gravity on a null surface
Wieland, W. (2017) · Classical and Quantum Gravity · doi:10.1088/1361-6382/aa8d06 · Cited by 74
Null Geodesic Congruences, Asymptotically-Flat Spacetimes and Their Physical Interpretation
Adamo, T., Kozameh, C. N., & Newman, E. T. (2009) · Living Reviews in Relativity · doi:10.12942/lrr-2009-6 · Cited by 75
The Geometry of Projective Reconstruction I: Matching Constraints and the Joint Image
Triggs, B. (1995) · Cited by 70
Twistor theory of hyper-Kähler metrics with hidden symmetries
Dunajski, M., & MASON, L. J. (2003) · Journal of Mathematical Physics · doi:10.1063/1.1588466 · Cited by 69
Anisotropic conformal infinity
Hořava, P., & Melby–Thompson, C. M. (2010) · General Relativity and Gravitation · doi:10.1007/s10714-010-1117-y · Cited by 74
Hyperboloidal evolution with the Einstein equations
Zenginoğlu, A. (2008) · Classical and Quantum Gravity · doi:10.1088/0264-9381/25/19/195025 · Cited by 69
On Einstein Manifolds of Positive Sectional Curvature
Gursky, M. J., & LeBrun, C. R. (1999) · Annals of Global Analysis and Geometry · doi:10.1023/a:1006597912184 · Cited by 69
Statistical Geometry in Quantum MechanicsPreprint
Brody, D. C., & Hughston, L. P. (1998) · Cited by 73
Scattering in black hole backgrounds and higher-spin amplitudes. Part I
Bautista, Y. F., Guevara, A., Kavanagh, C., & Vines, J. E. (2023) · Journal of High Energy Physics · doi:10.1007/jhep03(2023)136 · Cited by 75
MHV diagrams in momentum twistor space
Bullimore, M. R., MASON, L. J., & Skinner, D. B. (2010) · Journal of High Energy Physics · doi:10.1007/jhep12(2010)032 · Cited by 68
Spinor two-point functions in maximally symmetric spaces
Allen, B., & L�tken, C. A. (1986) · Communications in Mathematical Physics · doi:10.1007/bf01454972 · Cited by 68
Einstein-Yang-Mills isolated horizons: Phase space, mechanics, hair, and conjectures
Corichi, A., Nucamendi, U., & Sudarsky, D. (2000) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.62.044046 · Cited by 73
Barnett, S. M. (2014) · New Journal of Physics · doi:10.1088/1367-2630/16/9/093008 · Cited by 67
Beables/Observables in Classical and Quantum Gravity
Anderson, E. J. (2014) · Symmetry Integrability and Geometry Methods and Applications · doi:10.3842/sigma.2014.092 · Cited by 76
Rigorous steps towards holography in asymptotically flat spacetimes
Dappiaggi, C., Moretti, V., & Pinamonti, N. (2005) · Unitn Eprints Research (Università Degli Studi di Trento) · Cited by 67
Quantum mechanics of a spin particle in a curved spacetime with absolute time
Canarutto, D., Modugno, M., & Jadczyk, A. (1995) · Reports on Mathematical Physics · doi:10.1016/0034-4877(96)82487-6 · Cited by 66
SCATTERING OF MASSLESS DIRAC FIELDS BY A KERR BLACK HOLE
Häfner, D., & Nicolas, J.-P. (2004) · Reviews in Mathematical Physics · doi:10.1142/s0129055x04001911 · Cited by 61
Constants of geodesic motion in higher-dimensional black-hole spacetimes
Krtouš, P., Kubizňák, D., Page, D. N., & Vasudevan, M. (2007) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.76.084034 · Cited by 66
Outer curvature and conformal geometry of an imbedding
Carter, B. (1992) · Journal of Geometry and Physics · doi:10.1016/0393-0440(92)90043-z · Cited by 66
Smoothness at Null Infinity and the Structure of Initial Data
Friedrich, H. (2004) · Birkhäuser Basel eBooks · doi:10.1007/978-3-0348-7953-8_4 · Cited by 65
Optimal state for keeping reference frames aligned and the platonic solids
Kolenderski, P. L., & Demkowicz-Dobrzański, R. (2008) · Physical Review A · doi:10.1103/physreva.78.052333 · Cited by 64
Non-Abelian Tensor Multiplet Equations from Twistor Space
Saemann, C., & Wolf, M. (2014) · Communications in Mathematical Physics · doi:10.1007/s00220-014-2022-0 · Cited by 64
PROLONGATIONS OF GEOMETRIC OVERDETERMINED SYSTEMS
BRANSON, T., ČAP, A., EASTWOOD, M., et al. (2006) · International Journal of Mathematics · doi:10.1142/s0129167x06003655 · Cited by 64
Null cone evolution of axisymmetric vacuum space–times
Gómez, R., Papadopoulos, P., & Winicour, J. (1994) · Journal of Mathematical Physics · doi:10.1063/1.530848 · Cited by 64
The Weyl double copy from twistor spacePreprint
Chacón, E., Nagy, S., & White, C. D. (2021) · arXiv (Cornell University) · doi:10.1007/jhep05(2021)239 · Cited by 64
Covariant, algebraic, and operator spinors
Figueiredo, V. L. X., de Oliveira, E. C., & Rodrigues, W. A. (1990) · International Journal of Theoretical Physics · doi:10.1007/bf00674438 · Cited by 65
Carrollian amplitudes and celestial symmetries
MASON, L. J., Ruzziconi, R., & Srikant, A. Y. (2024) · Journal of High Energy Physics · doi:10.1007/jhep05(2024)012 · Cited by 63
Dirac fields and thermal effects in the de Sitter universe
Bartesaghi, P., Gazeau, J., Moschella, U., & Takook, M. V. (2001) · Classical and Quantum Gravity · doi:10.1088/0264-9381/18/21/302 · Cited by 61
Bičák, J., & Podolský, J. (1999) · Journal of Mathematical Physics · doi:10.1063/1.532982 · Cited by 63
Local boundary conditions for the Dirac operator and one-loop quantum cosmology
D'Eath, P. D., & Esposito, G. V. M. (1991) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.43.3234 · Cited by 61
BMS invariance and the membrane paradigm
Penna, R. F. (2016) · Journal of High Energy Physics · doi:10.1007/jhep03(2016)023 · Cited by 67
Energy conditions in arbitrary dimensions
Maeda, H., & Martínez, C. (2020) · Progress of Theoretical and Experimental Physics · doi:10.1093/ptep/ptaa009 · Cited by 63
Conformally invariant powers of the Laplacian — A complete nonexistence theorem
Gover, A. R., & Hirachi, K. (2004) · Journal of the American Mathematical Society · doi:10.1090/s0894-0347-04-00450-3 · Cited by 62
Structured spaces and their application to relativistic physics
Heller, M. C., & Sasin, W. (1995) · Journal of Mathematical Physics · doi:10.1063/1.530988 · Cited by 62
From Navier-Stokes to Maxwell via Einstein
Keeler, C. A., Manton, T., & Monga, N. (2020) · Journal of High Energy Physics · doi:10.1007/jhep08(2020)147 · Cited by 61
Dimensionally dependent tensor identities by double antisymmetrization
Edgar, S. B., & Höglund, A. (2002) · Journal of Mathematical Physics · doi:10.1063/1.1425428 · Cited by 61
Centrally extended BMS4 Lie algebroid
Glenn Barnich, A. (2017) · Journal of High Energy Physics · doi:10.1007/jhep06(2017)007 · Cited by 54
Poole, A., Skenderis, K., & Taylor, M. (2019) · Classical and Quantum Gravity · doi:10.1088/1361-6382/ab117c · Cited by 70
Greybody factors for black holes in four dimensions: Particles with spin
Mirjam Cvetič, B., & Larsen, F. K. (1998) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.57.6297 · Cited by 61
Excitation of quadratic quasinormal modes for Kerr black holes
Ma, S., & Yang, H. (2024) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.109.104070 · Cited by 60
Białynicki‐Birula, I. (1996) · Springer eBooks · doi:10.1007/978-1-4757-9742-8_38 · Cited by 62
Detection of spacetime fluctuation by a model interferometer
Percival, I. C., & Strunz, W. T. (1997) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.1997.0025 · Cited by 76
Subradiance via Entanglement in Atoms with Several Independent Decay Channels
Hebenstreit, M., Kraus, B., Ostermann, L., & Ritsch, H. (2017) · Physical Review Letters · doi:10.1103/physrevlett.118.143602 · Cited by 61
Vacaru, S. I. (1996) · Journal of Mathematical Physics · doi:10.1063/1.531406 · Cited by 59
The ‘unromantic pictures’ of quantum theory
Tumulka, R. (2007) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/40/12/s22 · Cited by 58
Concentric circles in WMAP data may provide evidence of violent pre-Big-Bang activityPreprint
Gurzadyan, V., & Penrose, R. (2010) · arXiv (Cornell University) · doi:10.48550/arxiv.1011.3706 · Cited by 59
Self-citationConformal and Einstein gravity from twistor actions
Adamo, T., & MASON, L. J. (2014) · Classical and Quantum Gravity · doi:10.1088/0264-9381/31/4/045014 · Cited by 58
SELF-DUAL YANG–MILLS: SYMMETRIES AND MODULI SPACE
Popov, A. D. (1999) · Reviews in Mathematical Physics · doi:10.1142/s0129055x99000350 · Cited by 58
Taylor, N., Boyle, M., Reisswig, C., et al. (2013) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.88.124010 · Cited by 57
Perturbative gauge theory at null infinity
Adamo, T., & Casali, E. (2015) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.91.125022 · Cited by 57
Stability for Linearized Gravity on the Kerr Spacetime
Andersson, L., Bäckdahl, T., Blue, P., & Ma, S. (2025) · Annals of PDE · doi:10.1007/s40818-024-00193-w · Cited by 89
On complete quaternionic-Kähler manifolds
LeBrun, C. (1991) · Duke Mathematical Journal · doi:10.1215/s0012-7094-91-06331-3 · Cited by 57
Notes on Projective Differential Geometry
Eastwood, M. (2008) · The IMA volumes in mathematics and its applications · doi:10.1007/978-0-387-73831-4_3 · Cited by 56
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