Functional central limit theorems and $P(phi)_{1}$-processes for the classical and relativistic Nelson models
Mathematical Physics
2020-11-25 v3 math.MP
Abstract
We construct -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.
Keywords
Cite
@article{arxiv.1605.01791,
title = {Functional central limit theorems and $P(phi)_{1}$-processes for the classical and relativistic Nelson models},
author = {Soumaya Gheryan and Fumio Hiroshima and Jozsef Lorinczi and Achref Majid and Habib Ouerdiane},
journal= {arXiv preprint arXiv:1605.01791},
year = {2020}
}
Comments
We revised Lemmas 3.4 and 3.10. We deleted Lemma 3.11. We added ref. [21,26]