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

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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.

Original languageEnglish
Article number18
JournalMathematical Physics Analysis and Geometry
Issue number2
Publication statusPublished - Jun 1 2020

All Science Journal Classification (ASJC) codes

  • Mathematical Physics
  • Geometry and Topology

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