Free Massless Fields as Infinite-Dimensional Representations of the Lorentz Group

Abstract

Free quantized massless field theories of arbitrary spin $L$ are investigated. The transverse potential in the radiation gauge is shown to transform as a nonunitary infinite-dimensional representation of the Lorentz group: $(L, 1)\oplus (L, -1)$ for integer spin and $(L+\frac{1}{2}, \frac{3}{2})\oplus (L+\frac{1}{2}, -\frac{3}{2})$ for integer +½ spin (Gel'fand and Shapiro's notation). Using Lorentz group theory, it is argued that free quantized massless field theories of spin >1 do not possess a stress-energy tensor $T^{\mu \nu }$.