What are the shortcomings of Klein Gordon equation and how it is overcome by Dirac equation?
Any solution of the free Dirac equation is, for each of its four components, a solution of the free Klein–Gordon equation. The Klein–Gordon equation does not form the basis of a consistent quantum relativistic one-particle theory. There is no known such theory for particles of any spin.
What is the spin of Dirac particle?
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 such as electrons and quarks for which parity is a symmetry.
Why is the Dirac equation important?
These fundamental physical constants reflect special relativity and quantum mechanics, respectively. Dirac’s purpose in casting this equation was to explain the behavior of the relativistically moving electron, and so to allow the atom to be treated in a manner consistent with relativity.
What are bilinear Covariants?
The wave functions themselves do not represent observables directly, but one can construct bilinear experessions of the wave functions which have the transformation properties of tensors. All Dirac matrices are simply constants and have the same value in all Lorentz frames.
What is the Dirac equation for a free fermion?
The Dirac equation describes the behaviour of spin-1/2 fermions in relativistic quantum field theory. For a free fermion the wavefunction is the product of a plane wave and a Dirac spinor, u(pµ): ψ(xµ)=u(pµ)e−ip·x(5.21) Substituting the fermion wavefunction, ψ, into the Dirac equation: (γµp µ−m)u(p) = 0 (5.22) 27
What is the Dirac equation in covariant form?
The Dirac equation can be thought of in terms of a “square root” of the Klein-Gordon equation. In covariant form it is written: iγ0 ∂t +i�γ · �� −m ψ =0 (iγµ∂ µ−m)ψ = 0 (5.13) where we have introduced the coefficients γµ=(γ0,�γ )=(γ0,γ1,γ2,γ3), which have to be determined.
Is the Dirac equation invariant under rotations and Lorentz boosts?
The Dirac equation should be invariant under Lorentz boosts and under rotations, both of which are just changes in the definition of an inertial coordinate system. Under Lorentz boosts, transforms like a 4-vector but the matrices are constant.
What are the four plane wave solutions to the Dirac equation?
The four plane wave solutions to the Dirac equation are where the four spinors are given by. is positive for solutions 1 and 2 and negative for solutions 3 and 4. The spinors are orthogonal