First order coherent boson states

We analyze the first order coherent states (and various sub-classes) over an arbitrary C*-Weyl algebra. Their normally ordered characteristic functions are expressed in terms of an infinite, positive-definite matrix, which exhibits an additional positive-definiteness condition if the states are classical. In the latter case the matrix elements are identified as moments of probability measures on C. By going over to measures of bC, the Bohr compactification of C, there arises a Bauer simplex of generalized classical coherent states. For macroscopic coherent states we give the GNS-representation, the central decomposition, and construct an extended Weyl formalism. (orig.)