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For an arbitrary (possibly infinite-dimensional) pre-symplectic test function space $$ (E, \sigma) $$ the family of Weyl algebras $$ \{\mathcal{W}(E, \hbar\sigma)\}_{\hbar\in\mathbb{R}} $$ , introduced in a previous work [1], is shown to constitute a continuous field of C *-algebras in the sense of Dixmier. Various Poisson algebras, given as (Fréchet-) *-algebras which are C *-norm-dense in $$ \mathcal{W}(E, 0) $$ , are constructed as domains for a Weyl quantization, which maps the classical onto the quantum mechanical Weyl elements. This kind of a quantization map is demonstrated to realize a continuous strict deformation quantization in the sense of Rieffel and Landsman. The quantization is proved to be equivariant under the automorphic actions of the full affine symplectic group. The relationship to formal field quantization in theoretical physics is discussed by suggesting a representation dependent direct field quantization in mathematically concise terms. [ABSTRACT FROM AUTHOR]

A closed, entirely quantum mechanical Josephson oscillator model is considered, consisting of two superconductors in tunneling contact, which weakly interact with the photon field. For each superconductor we use, for notational simplicity, the BCS model in the strong coupling approximation and restrict ourselves to Anderson?s quasi-spin formulation. The thermodynamic limit of the global (non-equilibrium) dynamics is formulated for a large variety of states. It arises a generalization of previously developed cocycle equations, connecting the collective behaviour of the two superconductors with the photon field dynamics. In the physically most interesting situations, where the two superconductors are in thermal equilibrium (below the critical temperature) at voltage difference V, we show, that for arbitrary initial states the outgoing multi-photon states are quantum optically all-order coherent and constitute an almost monochromatic radiation of frequency $ 2eV/\hbar $. Furthermore, we deduce in detail, how the collective behaviour of the superconductors influences the collective (that are the optical) features of the emitted microwave photons. [ABSTRACT FROM AUTHOR]