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...

study of Dirac operators, and Dirac type operators in analysis and geometry, together with their applications. Examples of Dirac type operators include...

In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including...

In mathematical analysis, the Dirac delta function (or δ distribution), also known as the unit impulse, is a generalized function on the real numbers...

The Dirac sea is a theoretical model of the electron vacuum as an infinite sea of electrons with negative energy, now called positrons. It was first postulated...

mathematical physics, the Dirac–von Neumann axioms give a mathematical formulation of quantum mechanics in terms of operators on a Hilbert space. They...

Paul Adrien Maurice Dirac (/dɪˈræk/ dih-RAK; 8 August 1902 – 20 October 1984) was an English mathematician and theoretical physicist who is considered...

\left\{\gamma ^{0},\gamma ^{1},\gamma ^{2},\gamma ^{3}\right\}\ ,} also called the Dirac matrices, are a set of conventional matrices with specific anticommutation...

manifold using the Laplace–de Rham operator. In four-dimensional flat spacetime, it is equivalent to four copies of the Dirac equation that transform into each...

becomes +iħ  preceding the 3-momentum operator. This operator occurs in relativistic quantum field theory, such as the Dirac equation and other relativistic...

indicates those twistor spinors which are also eigenspinors of the Dirac operator. The term is named after Wilhelm Killing. Another equivalent definition...

while the (absolute value of) Dirac operator retains the metric. On the other hand, the phase part of the Dirac operator, in conjunction with the algebra...

In mathematics, a Dirac spectrum, named after Paul Dirac, is the spectrum of eigenvalues of a Dirac operator on a Riemannian manifold with a spin structure...

first order operator d + δ {\displaystyle \mathrm {d} +\delta } is the Hodge–Dirac operator. When computing the Laplace–de Rham operator on a scalar function...

that this integrality could be explained if it were the index of the Dirac operator (which was rediscovered by Atiyah and Singer in 1961). The Atiyah–Singer...

of a Dirac operator. For example, the vacuum expectation value of the baryon number is given by the spectral asymmetry of the Hamiltonian operator. The...

Geometry of Dirac operators, p. 8, CiteSeerX 10.1.1.186.8445 Hörmander, L. (1983), The analysis of linear partial differential operators I, Grundl. Math...

of the determinant of a Dirac operator changes sign as one circumnavigates the circle. The eigenvalues of the Dirac operator come in pairs, and the sign...

Bra–ket notation, also called Dirac notation, is a notation for linear algebra and linear operators on complex vector spaces together with their dual...

position operator should necessarily be Dirac delta distributions, suppose that ψ {\displaystyle \psi } is an eigenstate of the position operator with eigenvalue...

forms: As the Dirac equation written so that the Dirac operator is purely Hermitian, thus giving purely real solutions. As an operator that relates a...

TBDE requires a particular form of mathematical consistency: the two Dirac operators must commute with each other. This is plausible if one views the two...

values in the Lie algebra g . {\displaystyle {\mathfrak {g}}\,.} The Dirac operator (in Feynman slash notation) is D /   = d e f   ∂ / + i A / {\displaystyle...

as second quantization. They were introduced by Paul Dirac. Creation and annihilation operators can act on states of various types of particles. For example...

found that on a spin manifold, the difference between the square of the Dirac operator and the tensor Laplacian (as defined on spinor fields) is given exactly...

a weakly elliptic first-order operator, such as the Dirac operator can square to become a strongly elliptic operator, such as the Laplacian. The composition...

In mathematical physics, the Dirac equation in curved spacetime is a generalization of the Dirac equation from flat spacetime (Minkowski space) to curved...

version of the Dirac–Kähler fermion. The naively discretized Dirac action in Euclidean spacetime with lattice spacing a {\displaystyle a} and Dirac fields ψ...

that this integrality could be explained if it were the index of the Dirac operator (which was rediscovered by Atiyah and Singer in 1961). The first announcement...

(2000), Dirac Operators in Riemannian Geometry, American Mathematical Society, ISBN 978-0-8218-2055-1 page 53 Friedrich, Thomas (2000), Dirac Operators in...