Higher-Order Approximation of Coherent State Dynamics in Self-Interacting Quantum Field Theories
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915839224053760 |
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| author | Ammari, Zied Malartre, Julien Zerzeri, Maher |
| author_facet | Ammari, Zied Malartre, Julien Zerzeri, Maher |
| contents | We study the propagation of coherent states in self-interacting bosonic quantum field theories in the semi-classical (mean-field) regime. Relying on Hepp's method and a detailed analysis of the associated classical and quantum field dynamics, non-linear and linear respectively, we construct an asymptotic expansion of arbitrary order for the quantum evolution of coherent states. The results are first established for the spatially cutoff $P(ϕ)_2$ model, under standard assumptions ensuring essential self-adjointness of the Hamiltonian and well-posedness of the classical flow, and are then extended to a class of non-polynomial analytic interactions. This work refines and generalizes earlier results, which identified only the leading-order term of the expansion. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_06026 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Higher-Order Approximation of Coherent State Dynamics in Self-Interacting Quantum Field Theories Ammari, Zied Malartre, Julien Zerzeri, Maher Mathematical Physics Analysis of PDEs 81R30, 81Q20, 81T08, 34A34, 35A01, 81V80 We study the propagation of coherent states in self-interacting bosonic quantum field theories in the semi-classical (mean-field) regime. Relying on Hepp's method and a detailed analysis of the associated classical and quantum field dynamics, non-linear and linear respectively, we construct an asymptotic expansion of arbitrary order for the quantum evolution of coherent states. The results are first established for the spatially cutoff $P(ϕ)_2$ model, under standard assumptions ensuring essential self-adjointness of the Hamiltonian and well-posedness of the classical flow, and are then extended to a class of non-polynomial analytic interactions. This work refines and generalizes earlier results, which identified only the leading-order term of the expansion. |
| title | Higher-Order Approximation of Coherent State Dynamics in Self-Interacting Quantum Field Theories |
| topic | Mathematical Physics Analysis of PDEs 81R30, 81Q20, 81T08, 34A34, 35A01, 81V80 |
| url | https://arxiv.org/abs/2603.06026 |