• 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...
    11 KB (1,619 words) - 04:55, 23 April 2025
  • study of Dirac operators, and Dirac type operators in analysis and geometry, together with their applications. Examples of Dirac type operators include...
    22 KB (3,393 words) - 22:49, 2 March 2025
  • 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...
    79 KB (13,114 words) - 00:17, 2 June 2025
  • Thumbnail for Dirac delta function
    In mathematical analysis, the Dirac delta function (or δ distribution), also known as the unit impulse, is a generalized function on the real numbers...
    96 KB (14,230 words) - 04:36, 14 May 2025
  • Thumbnail for Dirac sea
    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...
    14 KB (2,014 words) - 21:53, 23 August 2024
  • mathematical physics, the Dirac–von Neumann axioms give a mathematical formulation of quantum mechanics in terms of operators on a Hilbert space. They...
    4 KB (455 words) - 11:05, 7 May 2025
  • 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...
    11 KB (1,677 words) - 03:50, 25 May 2025
  • indicates those twistor spinors which are also eigenspinors of the Dirac operator. The term is named after Wilhelm Killing. Another equivalent definition...
    4 KB (481 words) - 19:43, 13 April 2025
  • Thumbnail for Paul Dirac
    Paul Adrien Maurice Dirac (/dɪˈræk/ dih-RAK; 8 August 1902 – 20 October 1984) was an English mathematical and theoretical physicist who is considered...
    92 KB (9,988 words) - 06:47, 21 May 2025
  • \left\{\gamma ^{0},\gamma ^{1},\gamma ^{2},\gamma ^{3}\right\}\ ,} also called the Dirac matrices, are a set of conventional matrices with specific anticommutation...
    61 KB (7,254 words) - 20:44, 10 May 2025
  • becomes +iħ  preceding the 3-momentum operator. This operator occurs in relativistic quantum field theory, such as the Dirac equation and other relativistic...
    15 KB (2,146 words) - 17:26, 28 May 2025
  • 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...
    8 KB (1,291 words) - 06:29, 14 April 2025
  • 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...
    20 KB (3,344 words) - 15:39, 29 May 2025
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    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...
    22 KB (3,693 words) - 02:35, 2 June 2025
  • 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...
    13 KB (1,959 words) - 20:14, 4 February 2025
  • 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...
    53 KB (7,553 words) - 10:43, 28 March 2025
  • 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...
    3 KB (511 words) - 11:29, 8 February 2025
  • 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...
    1 KB (134 words) - 07:29, 8 March 2024
  • Bra–ket notation, also called Dirac notation, is a notation for linear algebra and linear operators on complex vector spaces together with their dual...
    42 KB (6,334 words) - 08:54, 10 May 2025
  • 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...
    47 KB (8,807 words) - 17:38, 12 May 2025
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    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...
    13 KB (2,093 words) - 04:02, 18 April 2025
  • 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...
    35 KB (5,031 words) - 16:43, 18 May 2025
  • as second quantization. They were introduced by Paul Dirac. Creation and annihilation operators can act on states of various types of particles. For example...
    25 KB (4,463 words) - 03:42, 16 May 2025
  • Thumbnail for Two-body Dirac equations
    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...
    50 KB (8,789 words) - 02:48, 29 January 2024
  • Thumbnail for Dirac equation in curved spacetime
    In mathematical physics, the Dirac equation in curved spacetime is a generalization of the Dirac equation from flat spacetime (Minkowski space) to curved...
    13 KB (2,309 words) - 06:15, 31 March 2025
  • ,: 112  the Dirac constant: 275  : 726  : xv  (or Dirac's constant: 148  : 604  : 313 ), the Dirac h {\textstyle h} : xviii  (or Dirac's h {\textstyle...
    69 KB (6,164 words) - 05:06, 23 May 2025
  • and quantum mechanics. In quantum mechanics their importance lies in the Dirac–von Neumann formulation of quantum mechanics, in which physical observables...
    48 KB (8,156 words) - 10:24, 4 March 2025
  • values in the Lie algebra g . {\displaystyle {\mathfrak {g}}\,.} The Dirac operator (in Feynman slash notation) is D /   = d e f   ∂ / + i A / {\displaystyle...
    6 KB (1,385 words) - 15:45, 27 May 2025
  • position operator should necessarily be Dirac delta distributions, suppose that ψ {\displaystyle \psi } is an eigenstate of the position operator with eigenvalue...
    16 KB (2,611 words) - 18:41, 16 April 2025
  • Thumbnail for Magnetic monopole
    magnetic charge started with a paper by the physicist Paul Dirac in 1931. In this paper, Dirac showed that if any magnetic monopoles exist in the universe...
    73 KB (8,385 words) - 17:02, 29 April 2025