Generalized Dirac Equation for All Fermions?

[referframe]

The original Dirac Equation was for the electron, a particle of spin 1/2.

Is there a "Generalized Dirac Equation" that has been experimentally proven to work for all fermions, not just those of spin 1/2?

Thanks in advance.

 

[stevendaryl]

The original Dirac Equation was for the electron, a particle of spin 1/2.

Is there a "Generalized Dirac Equation" that has been experimentally proven to work for all fermions, not just those of spin 1/2?

Thanks in advance.

I don't have an answer, but I thought it was the case that the only fundamental fermions appearing in any current theory is spin-1/2 and spin-3/2 (which appears in supergravity). Higher-spin fermions are not used for anything, as far as I know. Of course, a composite particle can have an arbitrarily large spin.

 

[The_Duck]

The equivalent equation for spin-3/2 particles is the Rarita-Schwinger equation. I don't know if there is any sort of general equation to cover all half-integer spins.

 

[Avodyne]

It can be done for any particular value of the spin; Weinberg's QFT vol.1 explains how, in general, this works. Also, in string theory, you get infinite towers of fields with increasing spin (and mass).

 

[dextercioby]

The experimental part is an issue, there's no gravitino except on paper so far. Spin 5/2, 7/2, ... can't exist on paper, apparently, even though the general spin wave equation is as old as 1936 and the article by Dirac in PRSL. Then Pauli + Fierz, Bhabha, Duffin + Kemmer and last but not least Gel'fand and Yaglom.