Some continuous field quantizations, equivalent to the C*-Weyl quantization

Starting from a (possibly infinite dimensional) pre-symplectic space (E, or), we study a class of modified Weyl quantizations. For each value of the real Planck parameter h we have a C*-Weyl algebra W(E, ha), which altogether constitute a continuous field of C*-algebras, as discussed in previous works. For h = 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 quantization 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 continuous deformation quantization, equivalent to the Weyl quantization, in the sense of Rieffel and Landsman. Realizing the C*-algebraic quantization maps in regular and faithful Hilbert space representations leads to quantizations of the unbounded field expressions.