# Functional Central Limit Theorems and P(ϕ)1-Processes for the Relativistic and Non-Relativistic Nelson Models

Soumaya Gheryani, Fumio Hiroshima, József Lőrinczi, Achref Majid, Habib Ouerdiane

## 抄録

We construct P(ϕ)1-processes indexed by the full time-line, separately derived from the functional integral representations of the relativistic and non-relativistic Nelson models in quantum field theory. These two cases differ essentially by sample path regularity. Associated with these processes we define a martingale which, under an appropriate scaling, allows to obtain a central limit theorem for additive functionals of these processes. We discuss a number of examples by choosing specific functionals related to particle-field operators.

本文言語 英語 18 Mathematical Physics Analysis and Geometry 23 2 https://doi.org/10.1007/s11040-020-09345-3 出版済み - 6 1 2020

• 数理物理学
• 幾何学とトポロジー

## フィンガープリント

「Functional Central Limit Theorems and P(ϕ)<sub>1</sub>-Processes for the Relativistic and Non-Relativistic Nelson Models」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。