The set of Dirac spinors is a representation of the Lorentz algebra, whose generators are represented by the Dirac matrices γμ via the commutators, ie an element of the the Lorentz group is exp(12[γμ,γν]ωμν) where ωμν are the parameters.
The Dirac adjoint ˉψ=ψ†γ0 is defined such that the bilinear form ˉψψ is an invariant under transformations of the Lorentz group.
In the theory of compact Lie groups, we know there is a unique measure which induces a unique bilinear form on the Lie algebra.
Is this the same case for the Lorentz group? If not what are the other invariants? Is this the case for all (spin-) representations of the Lorentz group?