An Egorov-type Theorem for Analytic Wick Observables in Quantum Field Theory

We provide an exact Egorov-type formula, given by a convergent expansion in the semi-classical parameter $\varepsilon > 0$, for the propagation of a certain class of analytic Wick observables with super-exponentially decaying coefficients, under the action of a time-dependent quadratic Hamiltonian. This work generalizes a result established by S. Breteaux for polynomial symbols, and includes the spatially cutoff $P(φ)_2$ model, as well as a variant of the Höegh-Krohn model.