%0 Unpublished Work %A Gheryani, Soumaya %A Hiroshima, Fumio %A Lorinczi, Jozsef %A Majid, Achref %A Ouerdiane, Habib %D 2016 %T Functional central limit theorems and P(phi) 1 -processes for the classical and relativistic Nelson models %U https://repository.lboro.ac.uk/articles/preprint/Functional_central_limit_theorems_and_P_phi_1_-processes_for_the_classical_and_relativistic_Nelson_models/9384488 %2 https://repository.lboro.ac.uk/ndownloader/files/16996940 %K untagged %K Mathematical Sciences not elsewhere classified %X We construct $P(phi)_1$-processes indexed by the full time-line, separately derived from the functional integral representations of the classical Nelson model and relativistic Nelson model in quantum field theory. Associated with these processes we define a martingale which, under proper scaling, allows to obtain a central limit theorem for additive functionals of the two processes. We show a number of examples by choosing specific functionals related to particle-field operators. %I Loughborough University