# A basic question about the derivation of Dirac equation and other relativistic wavefunction equations

It is well-known that the Dirac equation is a "Relativistic wave equation" which describes all spin-1/2 massive particles such as electrons and quarks. The Dirac equation, as a system of linear differential equations, is derived from the relativistic energy-momentum quadratic relation. Definitely, there is the same derivation approach for the Weyl equation describing spin-1/2 massless particles, as it is just a special case of the Dirac equation.

On the other hand, in physics, the energy–momentum relation is the relativistic equation relating a particle's ("with any spin") rest mass, total energy, and momentum.

Now one may ask could other Relativistic wave equations, which describe other massive (and massless) particles with various spins, also be derived from the energy-momentum relation (by a derivation procedure similar to the Dirac equation)? If the answer in no, then one may ask why not?, Why only the Dirac equation is derived from such approach? Sorry if the question doesn't make sense somehow.

• In fact, it is well-known that the Dirac equation is not a relativistic wavefunction equation because has inconsistencies. In QFT, the Dirac equation is reinterpreted as a formal identity for a fermionic operator $\hat{\psi}$. It is not true that the Dirac equation is derived from the four-momentum. There is a hidden step that adds the half-spin. – juanrga Oct 15 '16 at 16:16
• As stated before the Dirac equation cannot be interpreted as a relativistic wavefunction equation, and the derivation of the equation doesn't follow from the four-momentum alone, but includes a hidden step that adds the non-zero spin. Wikipedia is not a scholar reference and that specific article you mention is particularly lacking. – juanrga Oct 15 '16 at 17:42
• @juanrga Sorry to say this, but truly your comments don't make sense. Before you've posted the same comments to this question: physics.stackexchange.com/questions/213491/…. It would be fine if you "check" the list of reliable and standard references mentioned in the articles noted in the question and my comments. You should present the relevant "References" for any of your personal claims and terminology. – user.3710634 Oct 15 '16 at 18:15
• Everything that I have written is well-known and found on standard textbooks. For instance, any advanced textbook on QM or virtually any textbook on QFT explains why the Dirac equation is not a valid relativistic wavefunction equation. – juanrga Oct 15 '16 at 18:45
• I am not going to give a list of "the page numbers and the exact names" of three dozens of textbooks explaining something very well-known: The Dirac equation is not a valid relativistic wavefunction equation. I will however mention Mandl-Shawn textbook, the Volume 1 of Weinberg textbook and the Vol. 4 of Landau-Lifshitz course to get some details on why the Dirac equation has to be physically re-interpreted as a formal equation for a fermionic operator $\hat{\psi}$. – juanrga Oct 15 '16 at 19:18