quantum mechanics, a Dirac operator is a differential operator that is a formal square root, or half-iterate, of a second-order operator such as a Laplacian...

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...

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

Paul Adrien Maurice Dirac (/dɪˈræk/; 8 August 1902 – 20 October 1984) was an English mathematical and theoretical physicist who is considered to be one...

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...

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

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

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...

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

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...

unviable. This was fixed by Dirac by taking the so-called square-root of the Klein-Gordon operator and in turn introducing Dirac matrices. In a modern context...

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...

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...

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

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...

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

In mathematics, a Dirac comb (also known as sha function, impulse train or sampling function) is a periodic function with the formula Ш   T ⁡ ( t )  ...

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...

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...

integral Dirac delta function Dirac comb Dirac measure Dirac operator Dirac algebra 5997 Dirac, an asteroid The various Dirac Medals Dirac (software) DiRAC supercomputing...

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...

all other fundamental interactions. Chirality for a Dirac fermion ψ is defined through the operator γ5, which has eigenvalues ±1; the eigenvalue's sign...

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

_{2}+\sigma _{2}\sigma _{1}=0} , so J 2 = − 1 {\displaystyle J^{2}=-1} ). The Dirac operator in this Clifford algebra is defined as ∇ ≡ σ 1 ∂ x + σ 2 ∂ y {\displaystyle...

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

and quantum mechanics. In quantum mechanics their importance lies in the Dirac–von Neumann formulation of quantum mechanics, in which physical observables...

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...

relation as we do for the bosonic field) in order to make the operators compatible with Fermi–Dirac statistics. By putting in the expansions for ψ ( x ) {\displaystyle...