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arXiv · 1605.01791

Functional central limit theorems and $P(phi)_{1}$-processes for the classical and relativistic Nelson models

Soumaya Gheryan·Fumio Hiroshima·Jozsef Lorinczi·Achref Majid·Habib Ouerdiane
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Abstract

We construct $P(phi)_1$-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.

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Soumaya Gheryan, Fumio Hiroshima, Jozsef Lorinczi, Achref Majid, Habib Ouerdiane. 2016-05-05. Functional central limit theorems and $P(phi)_{1}$-processes for the classical and relativistic Nelson models. https://arxiv.org/abs/1605.01791

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