The theta vacuum in $QCD$ is the standard vacuum, twisted by the exponential of the Chern-Simons term. But what is the quantum operator $U(g)$ for winding number $1$?\\

We construct $U(g)$ in this note. The Poincar\'{e} rotation generators commute with it only if they are augmented by the spin $\frac{1}{2}$ representation of the Lorentz group coming from large gauge transformations. This result is analogous to the `spin-isopin'
mixing result due to Jackiw and Rebbi \cite{Jackiw}, and Hasenfratz and 't Hooft \cite{hasenfratz} and a similar result in fuzzy physics \cite{Fuzzy}. \\

Hence states can drastically affect repreentations of observables. This fact is further shown by charged states dressed by infrared clouds. Following Mund, Rehren and Schroer \cite{MRS}, we find that Lorentz invariance is spontaneously broken in these sectors. This result has been extended earlier to $QCD$ (references \cite{nair} given in the Final Remarks) where even the global $QCD$ group is shown to be broken.\\

It is argued that the escort fields of \cite{MRS} are the Higgs fields for Lorentz and colour breaking. They are string-localised fields where the strings live in a union of de Sitter spaces. Their oscillations and those of the infrared clouds generate the associated Goldstone modes.