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  2. Dirac equation - Wikipedia

    en.wikipedia.org/wiki/Dirac_equation

    Dirac's purpose in casting this equation was to explain the behavior of the relativistically moving electron, thus allowing the atom to be treated in a manner consistent with relativity. He hoped that the corrections introduced this way might have a bearing on the problem of atomic spectra .

  3. Dirac equation in curved spacetime - Wikipedia

    en.wikipedia.org/wiki/Dirac_equation_in_curved...

    An alternative version of the Dirac equation whose Dirac operator remains the square root of the Laplacian is given by the Dirac–Kähler equation; the price to pay is the loss of Lorentz invariance in curved spacetime. Note that here Latin indices denote the "Lorentzian" vierbein labels while Greek indices denote manifold coordinate indices.

  4. Dirac algebra - Wikipedia

    en.wikipedia.org/wiki/Dirac_algebra

    In mathematical physics, the Dirac algebra is the Clifford algebra, ().This was introduced by the mathematical physicist P. A. M. Dirac in 1928 in developing the Dirac equation for spin-⁠ 1 / 2 ⁠ particles with a matrix representation of the gamma matrices, which represent the generators of the algebra.

  5. Wave function - Wikipedia

    en.wikipedia.org/wiki/Wave_function

    Soon after in 1928, Dirac found an equation from the first successful unification of special relativity and quantum mechanics applied to the electron, now called the Dirac equation. In this, the wave function is a spinor represented by four complex-valued components: [20] two for the electron and two for the electron's antiparticle, the ...

  6. Dirac spinor - Wikipedia

    en.wikipedia.org/wiki/Dirac_spinor

    In quantum field theory, the Dirac spinor is the spinor that describes all known fundamental particles that are fermions, with the possible exception of neutrinos.It appears in the plane-wave solution to the Dirac equation, and is a certain combination of two Weyl spinors, specifically, a bispinor that transforms "spinorially" under the action of the Lorentz group.

  7. Mathematical formulation of the Standard Model - Wikipedia

    en.wikipedia.org/wiki/Mathematical_formulation...

    It is possible to include both Dirac and Majorana mass terms in the same theory, which (in contrast to the Dirac-mass-only approach) can provide a “natural” explanation for the smallness of the observed neutrino masses, by linking the right-handed neutrinos to yet-unknown physics around the GUT scale [6] (see seesaw mechanism).

  8. Standard Model - Wikipedia

    en.wikipedia.org/wiki/Standard_Model

    The Dirac Lagrangian of the quarks coupled to the gluon fields is given by = ¯, where is a three component column vector of Dirac spinors, each element of which refers to a quark field with a specific color charge (i.e. red, blue, and green) and summation over flavor (i.e. up, down, strange, etc.) is implied.

  9. Gordon decomposition - Wikipedia

    en.wikipedia.org/wiki/Gordon_Decomposition

    In mathematical physics, the Gordon decomposition [1] (named after Walter Gordon) of the Dirac current is a splitting of the charge or particle-number current into a part that arises from the motion of the center of mass of the particles and a part that arises from gradients of the spin density.