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Starting from a (possibly infinite dimensional) pre-symplectic space (E, ), we study a class of modified Weyl quantizations. For each value of the real Planck parameter ~ we have a C*-Weyl algebra W(E,~ ), which altogether constitute a con- tinuous field of C*-algebras, as discussed in previous works. For ~ = 0 we construct a Frechet-Poisson algebra, densely contained in W(E,0), as the classical observables to be quantized. The quantized Weyl elements are decorated by so-called quantiza- tion factors, indicating the kind of normal ordering in specific cases. Under some assumptions on the quantization factors, the quantization map may be extended to the Frechet-Poisson algebra. It is demonstrated to constitute a strict and continu- ous deformation quantization, equivalent to the Weyl quantization, in the sense of Rieel and Landsman. Realizing the C*-algebraic quantization maps in regular and faithful Hilbert space representations leads to quantizations of the unbounded field expressions.

Squeezing processes are commonly described in terms of quadratic Hamiltonians, which generate unitary implementations of Bogoliubov transformations of the quantized electromagnetic field. Here the behaviour of the quasifree, the classical, and the coherent photon states under general squeezing Bogoliubov transformations is investigated. It is found that there is a great variety of mixed classical states, which remain classical under the squeezing operation, whereas each pure classical state becomes non-classical. Especially, some classical, microscopic first order coherent states remain classical and coherent of first order under one-mode squeezing. This contrasts squeezing of macroscopic coherent states.

By interpreting infinitely many two-level atoms as a mean field quantum lattice system in a recent paper the time evolution of the Dicke Maser model has been elaborated in terms of operator algebraic methods. Using these results, here the emitted radiation of the infinite Dicke model is investigated. It is shown how the collective behaviour of the atoms influences the quantized radiation, which for large times becomes classically coherent (in the sense of Glauber). The field modes which are (approximately) resonant with the level-splitting energy of the atoms are found to be the essential part of the generated coherent light, and thereby determine its macroscopic nature. Furthermore, the destruction and revival of coherence, the mean number of the emitted photons during the time evolution, as well as their spatial distribution are discussed.

Specifying their (normally ordered) characteristic functions we determine all states of the boson C*-Weyl algebra which satisfy Glauber's coherence condition and are not realizable as density operators in Fock space. The pure ones are shown to be just the eigenstates of the annihilation operators in their GNS-representations (in contrast to the Fock case) and are characterized in many equivalent manners. The central decomposition of an arbitrary coherent state has the macroscopic phase variable as parameter and is supported by the pure coherent states, which is in fact the only way for a maximal decomposition. The set of all coherent states with the same absolute factorizing function is proven to be a Bauer simplex. The appearence of a classical coherent field part is studied in detail in the GNS-representations and shown to correspond to an enlargement of the set of one boson states by just one additional mode.