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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.
GHERYAN, S. ... et al, 2016. Functional central limit theorems and P(phi) 1 -processes for the classical and relativistic Nelson models. arXiv:1605.01791
SMUR (Submitted Manuscript Under Review)
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This is a ArXiv pre-print. It is also available online at: http://arxiv.org/abs/1605.01791v1