The aim of this article is to study certain Lorentz invariant Lagrangians. The first of these Lagrangians could be related to a particle of spin 12 moving in a particular Yang–Mills gauge field. The second Lagrangian is related to the relativistic Newton–Coulomb problem. For each of these Lagrangians, we write the corresponding wave equations and determine the negative energy levels. The article concludes with the construction of a class of Lagrangians associated with pairs of particles, one of which has zero mass.

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