Functional central limit theorems and $P(phi)_{1}$-processes for the   classical and relativistic Nelson models
  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. 
Soumaya Gheryan, Fumio Hiroshima, Jozsef Lorinczi, Achref Majid, and   Habib Ouerdiane
math-ph math.MP