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The Dirac equation is () = If the Dirac equation is to be covariant, then it should have exactly the same form in all Lorentz frames: ′ ′ (′) ′ (′) = The two spinors and ′ should both describe the same physical field, and so should be related by a transformation that does not change any physical observables (charge, current, mass, etc.
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After it was introduced by Walter Thirring, [1] many authors tried to solve the massless case, with confusing outcomes. The correct formula for the two and four point correlation was finally found by K. Johnson; [2] then C. R. Hagen [3] and B. Klaiber [4] extended the explicit solution to any multipoint correlation function of the fields.
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.
Solutions to the euclidean Dirac equation Df = 0 are called (left) monogenic functions. Monogenic functions are special cases of harmonic spinors on a spin manifold. In 3 and 4 dimensions Clifford analysis is sometimes referred to as quaternionic analysis. When n = 4, the Dirac operator is sometimes referred to as the Cauchy–Riemann–Fueter ...
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It was first derived in 1928 by Oskar Klein and Yoshio Nishina, constituting one of the first successful applications of the Dirac equation. [1] The formula describes both the Thomson scattering of low energy photons (e.g. visible light ) and the Compton scattering of high energy photons (e.g. x-rays and gamma-rays ), showing that the total ...
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.