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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 electromagnetic interactions, it describes all spin-1/2 massive particles , called "Dirac particles", such as electrons and quarks for which parity is a symmetry .
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.
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.
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.
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.
The name of Dirac cone comes from the Dirac equation that can describe relativistic particles in quantum mechanics, proposed by Paul Dirac. Isotropic Dirac cones in graphene were first predicted by P. R. Wallace in 1947 [6] and experimentally observed by the Nobel Prize laureates Andre Geim and Konstantin Novoselov in 2005. [7]
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.
The defining property for the gamma matrices to generate a Clifford algebra is the anticommutation relation {,} = + = ,where the curly brackets {,} represent the anticommutator, is the Minkowski metric with signature (+ − − −), and is the 4 × 4 identity matrix.