We study, using Hepp's method, the propagation of coherent states for a general class of self interacting bosonic quantum field theories with spatial cutoffs. This includes models with non-polynomial interactions in the field variables. We show indeed that the time evolution of coherent states, in the classical limit, is well approximated by time-dependent affine Bogoliubov unitary transformations. Our analysis relies on a non-polynomial Wick quantization and a specific hypercontractive estimate.
"On the classical limit of self-interacting quantum field Hamiltonians with cutoffs." Hokkaido Math. J. 43 (3) 385 - 425, October 2014. https://doi.org/10.14492/hokmj/1416837571