The Lorentz group of special relativity has a variety of representations.
This is due to the non-compactness of the Lorentz group.
An important example of this is the inhomogeneous Lorentz group.
However, there are of course spinorial representations of the Lorentz group.
As usual, one introduces a connection field that allows us to gauge the Lorentz group.
This is one way to understand why the restricted Lorentz group is six dimensional.
A canonical reference; see chapters 1-6 for representations of the Lorentz group.
It corresponds to the representation of the Lorentz group, or rather, its part.
Such a circle corresponds to the space rotation parameters of the Lorentz group.
Language and terminology is used as in Representation theory of the Lorentz group.