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Accardi et al. proved a central limit theorem, based on the notion of projective independence. In this note we use the symmetric projective independence to present a new version of that result, where the limiting process is perturbed by the insertion of suitable test functions. Moreover we give a representation of the limit process in 1-mode type interacting Fock space.
We give a construction of the creation, annihilation and number processes on the Boolean Fock space by means of a quantum central limit theorem starting from creation, annihilation and number processes with discrete time.
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