1210.5441 (Zied Ammari et al.)

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

Zied Ammari, Maher Zerzeri

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.

View original: http://arxiv.org/abs/1210.5441