Lagrangian formulation for arbitrary spin. I. The boson case

Abstract

An explicit form is obtained for the Lagrangian of an arbitrary-spin boson field. This is achieved by introducing auxiliary field variables which are required to vanish in the free-field limit. For $s\le 4$ the results are found to be in agreement with those obtained by Chang. Canonical commutation rules are derived and the equations of motion are brought to first-order form, thereby facilitating the introduction of minimal electromagnetic coupling. It is found that, upon taking the Galilean limit, the ($6s+1$)-component Galilean-invariant theory of Hagen and Hurley results. The $g$ factor is found to be $\frac{1}{s}$, thereby confirming a long-standing conjecture.