Hokkaido Mathematical Journal

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

Zied AMMARI and Maher ZERZERI

Full-text: Open access

Abstract

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.

Article information

Source
Hokkaido Math. J., Volume 43, Number 3 (2014), 385-425.

Dates
First available in Project Euclid: 24 November 2014

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1416837571

Digital Object Identifier
doi:10.14492/hokmj/1416837571

Mathematical Reviews number (MathSciNet)
MR3282640

Zentralblatt MATH identifier
1304.81114

Subjects
Primary: 81R30: Coherent states [See also 22E45]; squeezed states [See also 81V80] 81T10: Model quantum field theories 81Q20: Semiclassical techniques, including WKB and Maslov methods 81V80: Quantum optics

Keywords
Classical limit Coherent states QFT Wick quantization $P(φ)_2$ model

Citation

AMMARI, Zied; ZERZERI, Maher. On the classical limit of self-interacting quantum field Hamiltonians with cutoffs. Hokkaido Math. J. 43 (2014), no. 3, 385--425. doi:10.14492/hokmj/1416837571. https://projecteuclid.org/euclid.hokmj/1416837571


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