Exploring a Tractable Lagrangian for Arbitrary Spin

Abstract

A simple Lagrangian is proposed that by the choice of the representation of SU(2), gives rise to field equations for arbitrary spin. In explicit examples it is shown, how the Klein-Gordon, the Dirac, and the Proca equation can be obtained from this Lagrangian. On the same footing, field equations for arbitrary spin are given. Finally, symmetries are discussed, the fields are quantized, their statistics is deduced, and Feynman rules are derived.