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Everything about Dirac operator
First-order differential linear operator on spinor bundle, whose square is the Laplacian
In mathematics and in quantum mechanics, a Dirac operator is a first-order differential operator that is a formal square root, or half-iterate, of a second-order differential operator such as a Laplacian. It was introduced in 1847 by William Hamilton and in 1928 by Paul Dirac. The question which concerned Dirac was to factorise formally the Laplace operator of the Minkowski space, to get an equation for the wave function which would be compatible with special relativity. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Dirac operatorA 5-minute orientation
- Skim a recent paper: Diffusion-driven instability of topological signals coupled by the Dirac operatorInfluential work since 2022
- Pick up a classic book: Dirac operators in representation theoryThe most-reprinted book on the subject
- Read the landmark paper: Dirac Operator and the Discrete SeriesCited 184 times
- Go sideways: Laplace operators in differential geometryA closely related topic
- Go sideways: Weitzenböck identityA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Dirac Operator and the Discrete Series
The dirac operator and gravitation
Bounds on the Wilson Dirac operator
The Dirac Operator on SUq(2)
Dirac Operator on Embedded Hypersurfaces
Sharp estimates and the Dirac operator
Eigenvalue bounds for the Dirac operator
An identification of the Dirac operator with the parity operator
🆕 Influential since 2022
Diffusion-driven instability of topological signals coupled by the Dirac operator
Spectral properties of the Dirac operator coupled with $$\delta $$-shell interactions
The three way Dirac operator and dynamical Turing and Dirac induced patterns on nodes and links
Scalar and mean curvature comparison via the Dirac operator
Band width estimates via the Dirac operator
📚 Books worth reading
Dirac operators in representation theoryJing-Song Huang · 2006
Symmetries of Maxwell's equationsVilʹgelʹm Ilʹich Fushchich, W.I. Fushchich · 1987- 📕Simmetrii͡a︡ uravneniĭ MaksvellaVilʹgelʹm Ilʹich Fushchich · 1983
Dirac-Operatoren in der Riemannschen GeometrieThomas Friedrich · 1997- 📕Spin-Strukturen und Dirac-Operatoren über pseudoriemannschen MannigfaltigkeitenHelga Baum · 1981
- 📕The determinant of the chiral Dirac operator and the eta invariantStephen Andrew Della Pietra · 1986
- 📕O espectro de uma classe de operadores Dirac e a topologia em 2 dimensõesLuiz C.L. Botelho, Centro Brasileiro de Pesquisas Físicas · 1998
The Dirac spectrumNicolas Ginoux · 2009
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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