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Dirac operator

Description: A Dirac operator is a first-order differential operator acting on spinor fields, studied in mathematical physics and geometry, often in relation to the Laplacian.
Wikidata ID: wiki/Q907439
OpenAlex ID: keywords/dirac-operator
Heat Kernels and Dirac Operators
1992 · Nicole Berline, Ezra Getzler, et al. · Springer eBooks · 1,753
The Dirac Equation
1992 · Bernd Thaller · Springer eBooks · 1,530
Invariance theory, the heat equation, and the Atiyah-Singer index theorem
1995 · Peter Gilkey · 1,456
The Index of Elliptic Operators: III
1968 · M. F. Atiyah, I. M. Singer · Annals of Mathematics · 1,255
The Index of Elliptic Operators: I
1968 · M. F. Atiyah, I. M. Singer · Annals of Mathematics · 1,141
R-Torsion and the Laplacian on Riemannian manifolds
1971 · D.B. Ray, I.M. Singer · Advances in Mathematics · 988
The Index of Elliptic Operators
1997 · MICHAEL F. ATIYAH · World scientific series in 20th century mathematics · 940
The Atiyah-Patodi-Singer Index Theorem
1993 · Richard Melrose · A K Peters/CRC Press eBooks · 923
Gravity coupled with matter and the foundation of non-commutative geometry
1996 · Alain Connes · Communications in Mathematical Physics · 820
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Clifford modules
1964 · M.F. Atiyah, R. Bott, et al. · Topology · 762
The generalized Douglas–Kroll transformation
2002 · Alexander Wolf, Markus Reiher, et al. · The Journal of Chemical Physics · 743
Spectral Theory of Ordinary Differential Operators
1987 · Joachim Weidmann · Lecture notes in mathematics · 735
On the heat equation and the index theorem
1973 · M. Atiyah, R. Bott, et al. · Inventiones mathematicae · 724
Positive scalar curvature and the Dirac operator on complete riemannian manifolds
1983 · Mikhael Gromov, H. Blaine Lawson · Publications mathématiques de l IHÉS · 691
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Clifford Algebras and Dirac Operators in Harmonic Analysis
1991 · J. Gilbert, M. Murray · Cambridge University Press eBooks · 642
More about exactly massless quarks on the lattice
1998 · Herbert Neuberger · Physics Letters B · 637
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Harmonic Spinors
1974 · Nigel Hitchin · Advances in Mathematics · 597
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Sturm—Liouville and Dirac Operators
1991 · B. M. Levitan, I. S. Sargsjan · Springer eBooks · 588
Riemannian Geometry and Geometric Analysis
2017 · Jürgen Jost · Universitext · 579
Quasirelativistic theory equivalent to fully relativistic theory
2005 · Werner Kutzelnigg, Wenjian Liu · The Journal of Chemical Physics · 565
Noncommutative geometry and reality
1995 · Alain Connes · Journal of Mathematical Physics · 545
The Index of Elliptic Operators: IV
1971 · M. F. Atiyah, I. M. Singer · Annals of Mathematics · 530
Random matrix theory and spectral sum rules for the Dirac operator in QCD
1993 · E.V. Shuryak, J.J.M. Verbaarschot · Nuclear Physics A · 512
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Axial anomalies and index theorems on open spaces
1978 · Constantine Callias · Communications in Mathematical Physics · 481
Exact two-component Hamiltonians revisited
2009 · Wenjian Liu, Daoling Peng · The Journal of Chemical Physics · 479
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Works count: 7,122
Citation count: 94,280
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