Elementary particles can be grouped into spin-classes and described by specific equations, see below:
Is there a general Lagrangian density from which all these equations can be derived?
A Lagrangian that allows for all types of spin, but after some gauge transformation settles down into a specific type?
Spin 1/2 -- Weyl equation: describes massless spin-1/2 particles -- Dirac equation: describes massive spin-1/2 particles (such as electrons) --Majorana equation: describes a massive Majorana particle -- Breit equation: describes two massive spin-1/2 particles (such as electrons) interacting electromagnetically to first order in perturbation theory
Spin 1 -- Maxwell equations: describe a photon (massless spin-1 particle)-- Proca equation: describes a massive spin-1 particle (such as W and Z bosons)-- Kemmer equation: an alternative equation for spin-0 and spin-1 particles (gauge fields)
Spin 3/2 --Rarita-Schwinger equation: describes a massive spin-3/2 particle
Arbitrary spin-- Bargmann-Wigner equations: describe free particles of arbitrary integral or half-integral spin.
Note: I'm not looking for a simple statement of Lagrangian formalism.