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

Zied Ammari (1) , Maher Zerzeri (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 LAGA - Laboratoire Analyse, Géométrie et Applications

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.

Mots clés: Classical limit; Coherent states; QFT; Wick quantization; P(')2 model

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]

Zied Ammari, Maher Zerzeri. On the classical limit of self-interacting quantum field Hamiltonians with cutoffs. Hokkaido Mathematical Journal, 2014, 43 (3), pp.385-425. ⟨10.14492/hokmj/1416837571⟩. ⟨hal-00763621⟩