Lagrange Formulation for Systems with Higher Spin

Prescriptions for constructing the generalized Lagrange function for a system with an arbitrary spin $S$ are presented. By the use of the spin projection operators introduced by Fronsdal, nonlocal field equations are constructed to describe these higher-spin systems. Then, auxiliary fields are introduced systematically to remove the nonlocalities appearing in these field equations. Lagrange functions describing systems with $S\le 4$ are constructed explicitly according to this new prescription. For $S=0, \frac{1}{2}, 1$, they agree with the well-known local Lagrange functions. For $S=\frac{3}{2} \mathrm{and} 2$, they are equivalent to the results previously obtained by Rarita and Schwinger, and by Fierz and Pauli. With the help of the quantum action principle, canonical quantizations are carried out and Green's functions are constructed. Some physical positiveness requirements are also verified.