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We study, using Hepp's method, the propagation of coherent states for ageneral class of self interacting bosonic quantum field theories with spatialcutoffs. This includes models with non-polynomial interactions in the fieldvariables. We show indeed that the time evolution of coherent states, in theclassical limit, is well approximated by time-dependent affine Bogoliubovunitary transformations. Our analysis relies on a non-polynomial Wickquantization and a specific hypercontractive estimate.

On the classical limit of self-interacting quantum field Hamiltonians with cutoffs