su(2) -expansion of the Lorentz algebra so(3,1 )

Abstract

We exploit the Iwasawa decomposition to construct coherent state representations of [Formula: see text], the Lorentz algebra in 3 + 1 dimensions, expanded on representations of the maximal compact subalgebra [Formula: see text]. Examples of matrix elements computation for finite dimensional and infinite-dimensional unitary representations are given. We also discuss different base vectors and the equivalence between these different choices. The use of the [Formula: see text]-matrix formalism to truncate the representation or to enforce unitarity is discussed.