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Dirac operator

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…

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Formal definition

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Dirac operator

Nodes54
Edges53
Triples44
Avg. degree1.96
Density0.037037
Components1

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Dirac operator

Top relations

related to Generalisations · 13
Dirac operator → Ck, Clifford, Dirac, Dolbeault, In, In Clifford, It, Rk, Rn, SL, Spin, The, This
related to Example 5 · 10
Dirac operator → Atiyah, Delta, Dirac, For, Gamma, Laplacian, Levi-Civita, R/4, Singer, The
related to Formal definition · 8
Dirac operator → Delta, Dirac, If, In, Laplace, Laplacian, Note, Riemannian
related to Example 2 · 4
Dirac operator → Consider, Dirac, It, The
related to Example 3 · 3
Dirac operator → Feynman, Feynman's Dirac, In
related to Example 4 · 3
Dirac operator → Another Dirac, Clifford, In
is a · 1
Dirac operator → first-order differential operator that is a formal square root
related to Example 1 · 1
Dirac operator → Dirac

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Important terminology

operator displaystyle dirac laplacian bundle delta clifford spinor space connection partial square manifold defined mathbb nabla differential equation function special

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Dirac operatoris afirst-order differential operator that is a formal square root0.90text
a Laplacianinstance ofof a second-order differential operator0.80text
Dirac operatorrelated to Example 1Dirac0.60section
Dirac operatorrelated to Example 2Consider0.60section
Dirac operatorrelated to Example 2It0.60section
Dirac operatorrelated to Example 2The0.60section
Dirac operatorrelated to Example 2Dirac0.60section
Dirac operatorrelated to Example 3Feynman's Dirac0.60section
Dirac operatorrelated to Example 3Feynman0.60section
Dirac operatorrelated to Example 3In0.60section
Dirac operatorrelated to Example 4Another Dirac0.60section
Dirac operatorrelated to Example 4Clifford0.60section

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